Yoshio Sano
The notion of $\mathcal{H}$-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of $\mathcal{H}$-matroids by the greedy algorithm. In this note, we give a characterization of some $\mathcal{H}$-matroids by rank functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We show that almost every matroid contains the rank-3 whirl $\mathcal{W}^3$ or the complete-graphic matroid $M(K_4)$ as a minor.
A matroid $\mathcal{M}$ on a set $E$ of elements has the $α$-partition property, for some $α>0$, if it is possible to (randomly) construct a partition matroid $\mathcal{P}$ on (a subset of) elements of $\mathcal{M}$ such that every independent set of $\mathcal{P}$ is independent in $\mathcal{M}$ and for any weight function $w:E\to\mathbb{R}_{\geq 0}$, the expected value of the optimum of the matroid secretary problem on $\mathcal{P}$ is at least an $α$-fraction of the optimum on $\mathcal{M}$. We show that the complete binary matroid, ${\cal B}_d$ on $\mathbb{F}_2^d$ does not satisfy the $α$-p…
We introduce the notion of sum-matroids and show its association with sum-rank metric codes. As a consequence, some results for sum-rank metric codes by Martínez-Peñas are generalized for sum-matroids. The sum-matroids generalize the notions of matroids and $q$-matroids. We define the generalized weights for sum-matroids and prove a Wei-type duality theorem which generalizes the analogous cases for matroids and q-matroids.
We show for each positive integer $a$ that, if $\mathcal{M}$ is a minor-closed class of matroids not containing all rank-$(a+1)$ uniform matroids, then there exists an integer $c$ such that either every rank-$r$ matroid in $\mathcal{M}$ can be covered by at most $r^c$ rank-$a$ sets, or $\mathcal{M}$ contains the GF$(q)$-representable matroids for some prime power $q$ and every rank-$r$ matroid in $\mathcal{M}$ can be covered by at most $cq^r$ rank-$a$ sets. In the latter case, this determines the maximum density of matroids in $\mathcal{M}$ up to a constant factor.
For a set of matroids $\mathcal{M}$, let $ex_\mathcal{M}(n)$ be the maximum size of a simple rank-$n$ matroid in $\mathcal{M}$. We prove that, for any finite field $\mathbb{F}$, if $\mathcal{M}$ is a minor-closed class of $\mathbb{F}$-representable matroids of bounded branch-width, then $\lim_{n \rightarrow \infty} ex_\mathcal{M}(n) / n$ exists and is a rational number, $Δ$. We also show that $ex_\mathcal{M}(n) - Δn$ is periodic when $n$ is sufficiently large and that $ex_\mathcal{M}$ is achieved by a subclass of $\mathcal{M}$ of bounded path-width.
The Las Vergnas' strong map conjecture, states that any strong map of oriented matroids $f:\mathcal{M}_1\rightarrow\mathcal{M}_2$ can be factored into extensions and contractions. The conjecture is known to be false due to a construction by Richter-Gebert, he find a non-factorizable strong map $f:\mathcal{M}_1\rightarrow\mathcal{M}_2$, however in his example $\mathcal{M}_1$ is not realizable. The problem that whether there exists a non-factorizable strong map between realizable oriented matroids still remains open. In this paper we provide a counterexample to the strong map conjecture on reali…
Given a mixed hypergraph $\mathcal{F}=(V,\mathcal{A}\cup \mathcal{E})$, functions $f,g:V\rightarrow \mathbb{Z}_+$ and an integer $k$, a packing of $k$ spanning mixed hyperarborescences is called $(k,f,g)$-flexible if every $v \in V$ is the root of at least $f(v)$ and at most $g(v)$ of the mixed hyperarborescences. We give a characterization of the mixed hypergraphs admitting such packings. This generalizes results of Frank and, more recently, Gao and Yang. Our approach is based on matroid intersection, generalizing a construction of Edmonds. We also obtain an algorithm for finding a minimum we…
A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.
The present note is a strengthening of a recent paper by K. Takazawa and Y. Yokoi (A generalized-polymatroid approach to disjoint common independent sets in two matroids, Discrete Mathematics (2019)). For given two matroids on $E$, under the same assumption in their paper to guarantee the existence of a partition of $E$ into $k$ common independent sets of the two matroids, we show that there exists a nearly uniform partition $\mathcal{P}$ of $E$ into $k$ common independent sets, where the difference of the cardinalities of any two sets in $\mathcal{P}$ is at most one.
For a simplicial complex ${\mathcal C}$ denote by $β({\mathcal C})$ the minimal number of edges from ${\mathcal C}$ needed to cover the ground set. If ${\mathcal C}$ is a matroid then for every partition $A_1, \ldots, A_m$ of the ground set there exists a set $S \in {\mathcal C}$ meeting each $A_i$ in at least $\frac{|A_i|}{β({\mathcal C})}$ elements. We conjecture that a slightly weaker result is true for the intersections of two matroids: if ${\mathcal D}={\mathcal P} \cap {\mathcal Q}$, where ${\mathcal P},{\mathcal Q}$ are matroids on the same ground set $V$ and $β({\mathcal P}), β({\mathc…
Interaction between skew-representability, tensor products, extension properties, and rank inequalities
本文通过张量积方法研究拟阵的斜可表示性，给出了其张量积刻画并证明判定该性质为上递归可枚举，同时推导出折叠斜可表示拟阵首个不源于公共信息性质的线性秩不等式。
A family of rank $4$ non-algebraic matroids with pseudomodular dual
针对Tic-Tac-Toe拟阵曾被视作对偶非代数的代数拟阵候选例的背景，本文构造了一类具备伪模、对偶非代数性质的无限拟阵族，推广了该拟阵。
We study the relationship between a q-analogue of matroids and linear codes with the rank metric in the vector space of matrices with entries in a finite field. We prove a Greene type identity for the rank generating function of these matroidal structures and the rank weight enumerator of these linear codes. As an application, we give a combinatorial proof of a MacWilliams type identity for Delsarte rank-metric codes.
The excluded minors for three classes of 2-polymatroids having special types of natural matroids
本文针对自然拟阵分别属于二元拟阵类、不含M(K4)-子式的拟阵类以及串并联网络圈拟阵连通分支类的三类2-多拟阵，求出了它们的排除子式，并引入k-自然拟阵证明这些类在2-对偶下封闭。
We give polynomial-time randomized algorithms for computing the girth and the cogirth of binary matroids that are low-rank perturbations of graphic matroids.
Rank functions and invariants of delta-matroids
本文通过秩函数公理化δ-拟阵，研究其秩生成函数，并利用洛伦兹多项式理论证明相关取值的对数凹性。
Oriented matroid structures on rank 3 root systems
本文证明了秩3仿射根系在满足Weyl群等变且限制为秩2子系统通常拟阵结构的条件下，具有唯一的定向拟阵结构，并将该唯一性结论推广至有限根系及“干净”秩3根系。
We show for each positive integer $a$ that, if $\cM$ is a minor-closed class of matroids not containing all rank-$(a+1)$ uniform matroids, then there exists an integer $n$ such that either every rank-$r$ matroid in $\cM$ can be covered by at most $r^n$ sets of rank at most $a$, or $\cM$ contains the $\GF(q)$-representable matroids for some prime power $q$, and every rank-$r$ matroid in $\cM$ can be covered by at most $r^nq^r$ sets of rank at most $a$. This determines the maximum density of the matroids in $\cM$ up to a polynomial factor.
In a recent paper, Bruhn, Diestel, Kriesell and Wollan (arXiv:1003.3919) present four systems of axioms for infinite matroids, in terms of independent sets, bases, closure and circuits. No system of rank axioms is given. We give an easy example showing that rank function of an infinite matroid may not suffice to characterize it. We present a system of axioms in terms of relative rank.
The Folkman-Lawrence topological representation theorem, which states that every (loop-free) oriented matroid of rank $r$ can be represented as a pseudosphere arrangement on the $(r-1)$-dimensional sphere $S^{r-1}$, is one of the most outstanding results in oriented matroid theory. In this paper, we provide a lower-dimensional version of the topological representation theorem for uniform matroid polytopes of rank $4$. We introduce $2$-weak configurations of points and pseudocircles ($2$-weak PPC configurations) on $S^2$ and prove that every uniform matroid polytope of rank $4$ can be represent…
Matroid polytopes with small rank
本文定义了格多面体的秩，并刻画了秩至多为三的拟阵独立多面体与图拟阵基多面体，进而探讨了它们与序多面体、稳定集多面体和边多面体的联系。
Given an $\Bbb{F}$-represented matroid $(M,ρ)$ with the ground set $[m]$, the representation $ρ$ naturally defines a hyperplane arrangement $\mathcal{A}_ρ$. We will study its parallel translates $\mathcal{A}_{ρ,{g}}$ of $\mathcal{A}_ρ$ for all ${ g}\in \mathbb{F}^m$. Its intersection semi-lattices $L(\mathcal{A}_{ρ,{ g}})$ and the characteristic polynomials $χ(\mathcal{A}_{ρ,{ g}},t)$ will be classified by the intersection lattice of the derived arrangement $\mathcal{A}_{δρ}$, which is a hyperplane arrangement associated with the derived matroid $(δM,δρ)$ and also known as the discriminantal a…
We present a strengthening of the countable Menger theorem (edge version) of R. Aharoni. Let $ D=(V,A) $ be a countable digraph with $ s\neq t\in V $ and let $\mathcal{M}=\bigoplus_{v\in V}\mathcal{M}_v $ be a matroid on $ A $ where $ \mathcal{M}_v $ is a finitary matroid on the ingoing edges of $ v $. We show that there is a system of edge-disjoint $ s \rightarrow t $ paths $ \mathcal{P} $ such that the united edge set of the paths is $ \mathcal{M} $-independent, and there is a $ C \subseteq A $ consists of one edge from each element of $ \mathcal{P} $ for which $ \mathsf{span}_{\mathcal{M}}(…
Free products, principal sums, bipartition complete matroids and the linking operation $(\mathcal{M}_{SP} \vee \mathcal{M}_{PQ}) \times (S \uplus Q)$
本文研究二分完全拟阵，利用链接运算构造任意拟阵的二分扩张并证明其性质，还证明二分完全性对拟阵子式稳定，给出自由积与主和拟阵的极小分解。
Matroids with different configurations and the same $\mathcal{G}$-invariant
本文研究拟阵构型与$\mathcal{G}$-不变量之间的信息差异，提出了多种构造具有不同构型但相同$\mathcal{G}$-不变量的拟阵的方法，并提供了开发更多构造的工具。
We show that, if $k$ and $\ell$ are positive integers and $r$ is sufficiently large, then the number of rank-$k$ flats in a rank-$r$ matroid $M$ with no $U_{2,\ell+2}$-minor is less than or equal to number of rank-$k$ flats in a rank-$r$ projective geometry over GF$(q)$, where $q$ is the largest prime power not exceeding $\ell$.
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that $s(n) \sim m(n)$, where $m(n)$ denotes the number of matroids on a fixed groundset of size $n$, and $s(n)$ the number of sparse paving matroids. In an earlier paper, we showed that $\log s(n) \sim \log m(n)$. The bounds that we used for that result were dominated by matroids of rank $r\approx n/2$. In this paper we consider the relation between the number of sparse paving matroids $s(n,r)$ and the number of matroids $m(n,r)$ on a fixed groundset of size $n$ of fixed rank $r$. In particular, we show tha…
In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $\mathcal M$ such that its corresponding toric ideal $I_{\mathcal M}$ is a complete intersection. Secondly, we handle with the problem of detecting minors of a matroid $\mathcal M$ from a minimal set of binomial generators of $I_{\mathcal M}$. In particular, given a minimal set of binomial generators of $I_{\mathcal M}$ we provide a necessary condition for $\mathcal M$ to have a minor isomorphic to $\mathcal U_{d,2d}$ for $d \geq 2$. This condition is proved to be suff…
Let $\mathcal{N}$ be a set of matroids. A matroid $M$ is strictly $\mathcal{N}$-fragile if $M$ has a member of $\mathcal{N}$ as minor and, for all $e \in E(M)$, at least one of $M\backslash e$ and $M/e$ has no minor in $\mathcal{N}$. In this paper we give a structural description of the strictly $\{U_{2,5},U_{3,5}\}$-fragile matroids that have six inequivalent representations over $\mathrm{GF}(5)$. Roughly speaking, these matroids fall into two classes. The matroids without an $\{X_8, Y_8, Y_8^{*}\}$-minor are constructed, up to duality, from one of two matroids by gluing wheels onto specified…
Binomial Random Matroids
研究二项随机集合定义模体的概率，证明当概率p满足特定条件时，模体出现的概率趋于1或指数衰减，同时分析稀疏铺砌模体和贪心算法对模体计数的影响。
An 'induced restriction' of a simple binary matroid $M$ is a restriction $M|F$, where $F$ is a flat of $M$. We consider the class $\mathcal{M}$ of all simple binary matroids $M$ containing neither a free matroid on three elements (which we call a 'claw'), nor a Fano plane as an induced restriction. We give an exact structure theorem for this class; two of its consequences are that the matroids in $\mathcal{M}$ have unbounded critical number, while the matroids in $\mathcal{M}$ not containing the clique $M(K_5)$ as an induced restriction have critical number at most $2$.
In this paper we describe a parallel algorithm for generating all non-isomorphic rank $3$ simple matroids with a given multiplicity vector. We apply our implementation in the HPC version of GAP to generate all rank $3$ simple matroids with at most $14$ atoms and a splitting characteristic polynomial. We have stored the resulting matroids alongside with various useful invariants in a publicly available, ArangoDB-powered database. As a byproduct we show that the smallest divisionally free rank $3$ arrangement which is not inductively free has $14$ hyperplanes and exists in all characteristics di…
For each proper minor-closed subclass $\cM$ of the $\GF(q^2)$-representable matroids containing all simple $\GF(q)$-representable matroids, we give, for all large $r$, a tight upper bound on the number of points in a rank-$r$ matroid in $\cM$, and construct a rank-$r$ matroid in $\cM$ for which equality holds. As a consequence, we give a tight upper bound on the number of points in a $\GF(q^2)$-representable, rank-$r$ matroid with no $\PG(k,q^2)$-minor.
Leclerc and Zelevinsky, motivated by the study of quasi-commuting quantum flag minors, introduced the notions of strongly separated and weakly separated collections. These notions are closely related to the theory of cluster algebras, to the combinatorics of the double Bruhat cells, and to the totally positive Grassmannian. A key feature, called the purity phenomenon, is that every maximal by inclusion strongly (resp., weakly) separated collection of subsets in $[n]$ has the same cardinality. In this paper, we extend these notions and define $\mathcal{M}$-separated collections for any oriented…
Over a decade ago De Loera, Haws and Köppe conjectured that Ehrhart polynomials of matroid polytopes have only positive coefficients and that the coefficients of the corresponding $h^*$-polynomials form a unimodal sequence. The first of these intensively studied conjectures has recently been disproved by the first author who gave counterexamples in all ranks greater or equal to three. In this article we complete the picture by showing that Ehrhart polynomials of matroids of lower rank have indeed only positive coefficients. Moreover, we show that they are coefficient-wise bounded by the Ehrhar…
Let $M$ be a matroid satisfying a matroidal analogue of the Cayley-Bacharach condition. Given a number $k \ge 2$, we show that there is no nontrivial bound on ranks of a $k$-tuple of flats covering the underlying set of $M$. This addresses a question of Levinson-Ullery motivated by earlier results which show that bounding the number of points satisfying the Cayley-Bacharach condition forces them to lie on low-dimensional linear subspaces. We also explore the general question what matroids satisfy the matroidal Cayley-Bacharach condition of a given degree and its relation to the geometry of gen…
We give a cohomological interpretation of the Heaviside filtration on the Varchenko--Gelfand ring of a pair $(\mathcal{A},\mathcal{K})$, where $\mathcal{A}$ is a real hyperplane arrangement and $\mathcal{K}$ is a convex open subset of the ambient vector space. This builds on work of the first author, who studied the filtration from a purely algebraic perspective, as well as work of Moseley, who gave a cohomological interpretation in the special case where $\mathcal{K}$ is the ambient vector space. We also define the Gelfand--Rybnikov ring of a conditional oriented matroid, which simultaneously…
The $\mathit{growth\ rate\ function}$ for a nonempty minor-closed class of matroids $\mathcal{M}$ is the function $h_{\mathcal{M}}(n)$ whose value at an integer $n \ge 0$ is defined to be the maximum number of elements in a simple matroid in $\mathcal{M}$ of rank at most $n$. Geelen, Kabell, Kung and Whittle showed that, whenever $h_{\mathcal{M}}(2)$ is finite, the function $h_{\mathcal{M}}$ grows linearly, quadratically or exponentially in $n$ (with base equal to a prime power $q$), up to a constant factor. We prove that in the exponential case, there are nonnegative integers $k$ and $d \le \…
Orlik-Solomon algebras determine the Tutte polynomials of matroids of rank at most three
本文证明了Falk关于秩为3的简单拟阵的Orlik-Solomon代数确定其Tutte多项式的猜想，且该结论对所有秩不超过3的简单拟阵均成立。
We investigate the set of excluded minors of connectivity 2 for the class of frame matroids. We exhibit a list $\mathcal{E}$ of 18 such matroids, and show that if $N$ is such an excluded minor, then either $N \in \mathcal{E}$ or $N$ is a 2-sum of $U_{2,4}$ and a 3-connected non-binary frame matroid.
The Theta rank of a finite point configuration $V$ is the maximal degree necessary for a sum-of-squares representation of a non-negative linear function on $V$. This is an important invariant for polynomial optimization that is in general hard to determine. We study the Theta rank and levelness, a related discrete-geometric invariant, for matroid base configurations. It is shown that the class of matroids with bounded Theta rank or levelness is closed under taking minors. This allows for a characterization of matroids with bounded Theta rank or levelness in terms of forbidden minors. We give t…
The free $m$-cone of a matroid and its $\mathcal{G}$-invariant
本文通过引入无环拟阵的自由 m-锥 Q_m(M)，构造了具有相同 G-不变量但构型不同的新拟阵对，并定义了决定 Q_m(M) 的 Tutte 多项式的新拟阵不变量。
Matroid is a generalization of many fundamental objects in combinatorial mathematics , and matroid intersection problem is a classical subject in combinatorial optimization . However , only the intersection of two matroids are well understood . The solution of the intersection problem of more than three matroids is proved to be \textbf{NP-hard} . We will give a lower bound estimate on the maximal cardinality of the common independent sets in matroid intersections . We will also study some properties of the intersection of more than two matroids and deduce some analogous results for Edmonds' Mi…
Average plane-size in complex-representable matroids
本文研究复可表示拟阵中平面平均大小，借助Ben Lund关于秩k平面数量的估计定理，证明秩4及一般高秩情形下相应平均值受绝对常数或仅依赖参数的常数约束。
Rigidity and reconstruction in matroids of highly connected graphs
本文研究了图matroid的刚性和重构性质，证明了在无界情况下，Whitney性质与Lovász-Yemini性质等价，并展示了1-可扩展图matroid家族的重构特性。
Matroid adjoints and the minimum rank of zero-nonzero matrix patterns
本文将零-非零模式的最小秩问题推广至拟阵，通过定义基本模式与拟阵伴随，揭示了三角形数与拟阵最小秩差距的对偶关系，并证明了最小秩拟阵的唯一性及其在不同域上对可表示性的依赖。
Representability of $q$-matroids via rank-metric codes
本文研究了 $q$-matroids 的多线性表示性，通过排序度码的自然可除性条件定义了 $m$-多线性表示性，并证明了非平凡均匀 $q$-matroids 无法纯多线性表示，且非帕普斯 $q$-matroid 的块大小至少为 9。
In 1977 Stanley conjectured that the $h$-vector of a matroid independence complex is a pure $O$-sequence. In this paper we use lexicographic shellability for matroids to motivate a combinatorial strengthening of Stanley's conjecture. This suggests that a pure $O$-sequence can be constructed from combinatorial data arising from the shelling. We then prove that our conjecture holds for matroids of rank at most four, settling the rank four case of Stanley's conjecture. In general, we prove that if our conjecture holds for all rank $d$ matroids on at most $2d$ elements, then it holds for all matro…
In this note we prove a lower bound for the rank of 2-dimensional generic rigidity matroid for regular graphs of degree four and five. Also, we give examples to show the order of the bound we give is sharp.
A common generalization to strengthenings of Drisko's Theorem for intersections of two matroids
本文证明了在同一基集上的两个拟阵中，存在大小为n的部分彩虹独立集，共同推广了二部图和拟阵交的彩虹匹配结果。
Let $M$ be an arbitrary matroid with circuits $\mathcal{C}(M)$. We propose a definition of a derived matroid $δM$ that has as its ground set $\mathcal{C}(M)$. Unlike previous attempts of such a definition, our definition applies to arbitrary matroids, and is completely combinatorial. We prove that the rank of $δM$ is bounded from above by $|M|-r(M)$, that it is connected if and only if $M$ is connected. We compute examples including the derived matroids of uniform matroids, the Vámos matroid and the graphical matroid $M(K_4)$. We formulate conjectures relating our construction to previous defi…
Extensions and Deletions of matroid classes closed under flats
研究在平面下封闭的拟阵类（遗传类）的扩展类与删除类的禁止平面性质，证明了若遗传类有有限个禁止平面，则其扩展类的禁止平面有界秩，并对GF(q)-可表示拟阵（q=2,3）建立了删除类的类似结果。
In this paper we investigate a family of matroids introduced by Ardila and Billey to study one-dimensional intersections of complete flag arrangements of $\mathbb{C}^n$. The set of lattice points $P_n$ inside the equilateral triangle $S_n$ obtained by intersecting the nonnegative cone of $\mathbb{R}^3$ with the affine hyperplane $x_1 + x_2 + x_3 = n-1$ is the ground set of a matroid $\mathcal{T}_n$ whose independent sets are the subsets $S$ of $P_n$ satisfying that $|S \cap P| \le k$ for each translation $P$ of the set $P_k$. Here we study the structure of the matroids $\mathcal{T}_n$ in conne…
We consider $q$-matroids and their associated classical matroids derived from Gabidulin rank-metric codes. We express the generalized rank weights of a Gabidulin rank-metric code in terms of Betti numbers of the dual classical matroid associated to the $q$-matroid corresponding to the code. In our main result, we show how these Betti numbers and their elongations determine the generalized weight polynomials for $q$-matorids, in particular, for the Gabidulin rank-metric codes. In addition, we demonstrate how the weight distribution and higher weight spectra of such codes can be determined direc…
Real-rootedness and ultra log-concavity of rank-two matroid Ehrhart $h^*$-polynomials
本文证明秩二拟阵在特定条件下Ehrhart $h^*$-多项式的实根性，给出反例否证猜想，并证明超对数凹性及单峰性。
On plane rigidity matroids
本文研究了二维刚性模体族的性质，证明了R和H是唯一与代数曲线相关的2-刚性族，并揭示了立方图的定向特性。
The excluded minors for $k$-polymatroids with binary $k$-natural matroids
本文研究了具有二元 $k$-自然拟阵的 $k$-多拟阵类的排除子式问题，确定了当 $k \geq 3$ 时该类的排除子式集合是有限的，其中 $\widetilde{\mathcal{C}}'_3$ 有 $12$ 个，$k > 3$ 时有 $k+7$ 个。
Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial dual…
The polytope of all matroids in ranks 2 and 3
本文给出了2和3级matroid多面体Ω_{r,n}的显式递归构造，实现了其计算，并计算了所有2级和3级matroid的Schubert展开。
Real-rootedness of Kazhdan--Lusztig polynomials of sparse paving matroids
本文证明稀疏铺砌拟阵的非常数Kazhdan--Lusztig多项式仅有简单负零点，并给出均匀拟阵多项式与稀疏铺砌拟阵多项式的严格交错关系。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。