An Extension of the Foata Map to Standard Young Tableaux
Jim Haglund, Laura Stevens
我们定义了一个反演统计的标准杨tableaux。我们证明了这个统计量在SYT（λ）上具有与主指标统计量相同的分布，通过展示SYT（λ）上的双射，在排列上的Foata映射的精神。
We define an inversion statistic on standard Young tableaux. We prove that this statistic has the same distribution over SYT(λ) as the major index statistic by exhibiting a bijection on SYT(λ) in the spirit of the Foata map on permutations.
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Generalized Dumont-Foata polynomials and alternative tableaux
Dumont和Foata在1976年引入了Genocchi数的一个三变量对称加细，它满足一个简单的递归关系。后来杜蒙考虑了具有许多类似性质的六变量推广。它们推广了许多已知的整数序列，并且它们的母函数可以展开为Jacobi连分数。我们在这里给出一个新的组合解释的六变量多项式的替代tableaux介绍Viennot。一个强大的工具，列举替代tableaux是所谓的“矩阵Ancestion”，并使用此，我们表明，我们的组合解释自然会导致一个新的证明的连分数扩展。
We present combinatorial bijections and identities between certain skew Young tableaux, Dyck paths, triangulations, and dissections.
In this paper we first present summation formulas for $k$-order Eulerian polynomials and $1/k$-Eulerian polynomials. We then present combinatorial expansions of $(c(x)D)^n$ in terms of inversion sequences as well as $k$-Young tableaux, where $c(x)$ is a differentiable function in the indeterminate $x$ and $D$ is the derivative with respect to $x$. We define the $g$-indexes of $k$-Young tableaux and Young tableaux, which have important applications in combinatorics. By establishing some relations between $k$-Young tableaux and standard Young tableaux, we express Eulerian polynomials, second-ord…
Cylindric Young Tableaux and their Properties
杨格图是20世纪90年代首次出现的组合对象。作为经典的杨格画面概念的自然扩张，它们被多次使用，最著名的是Gessel和Krattenthaler以及Alexander Postnikov。尽管如此，对圆柱形的杨场景知之甚少。本文是对这一天体性质的研究。在本文中，我们将Robinson-Schensted-Knuth对应关系（一种关于规则Young tableaux的著名且非常有用的双射）扩展为圆柱形tableaux对之间的对应关系。利用这种对应关系，我们得到了关于柱面tableaux的进一步结果。然后，我们建立了一个解释的圆柱形tableaux在涉及大理石传递的游戏。接下来，我们展示了一个通用的方法来使用有关圆柱形tableaux的结果，以证明结果斜杨tableaux。最后，我们注意到克努特等价和其类似的圆柱tableaux。
We survey some recent works on standard Young tableaux of bounded height. We focus on consequences resulting from numerous bijections to lattice walks in Weyl chambers.
Using lattice path counting arguments, we reproduce a well known formula for the number of standard Young tableaux. We also produce an interesting new formula for tableaux of height $\leq 3$ using the Fourier methods of Ault and Kicey.
The flush statistic on semistandard Young tableaux
在本说明中，定义了Young tableaux的统计量，该统计量对Casselman-Shalika公式所需的数据进行编码。
Diagonal vectors of shifted Young tableaux
我们研究的标准杨tableaux的移位形状的对角线上的条目所形成的向量。这样的向量与某些整多面体的整格点是双射的，这些整多面体是单形的Minkowski和。我们还描述了这些多面体的顶点，并构造相应的移动杨tableaux。
This paper completely characterizes the standard Young tableaux that can be reconstructed from their sets or multisets of $1$-minors. In particular, any standard Young tableau with at least $5$ entries can be reconstructed from its set of $1$-minors.
Enumeration of Standard Young Tableaux
一份调查文件，将作为一个章节出现在即将出版的《枚举手册》中。
A `nice' bijection for a content formula for skew semistandard Young tableaux
基于Schützenberger的疏散和jeu de taquin的一个修正，给出了有界项的反向半标准Young表的生成函数与所有半标准Young表的生成函数之间的一个恒等式的双射证明.这解决了Richard Stanley的书《枚举组合数学2》中的练习7.102 b。
Identities for the number of standard Young tableaux in some $(k,\ell)$ hooks
闭公式是已知的$S(k,0;n)$，数量标准的杨tableaux的大小$n$和最多$k$部分，其中$1\le k\le 5$。在这里，我们研究的模拟问题，$S(k,\ell;n)$，标准的年轻tableaux的大小$n$的数量包含在$(k,\ell)$钩。我们推导了$k+\ell\le 4$情形的一些公式。
Alternating permutations with restrictions and standard Young tableaux
本文通过Yamanouchi词的中间结构，给出了长度为$2n$的4123-避免的上下交替排列集与形状为$(n,n,n)$的标准Young表集之间的双射，以及长度为$2n-1$的4123-避免的上下交替排列集与形状为$(n+1, n, n-1)$的移位标准Young表集之间的双射.此外，通过给出4123-避免上下交替排列与标准Young表之间的双射，得到了4123-避免上下交替排列的偶数和奇数长度的计数.
Counting Descents in Standard Young Tableaux
本文讨论了某些形状的标准杨氏图的下降数分布。一个简单的显式公式，提出了任何形状的两行，与任何指定数量的下降。对于三行中有一个单元的形状，给出了递归公式，并在某些情况下求解。
Using Symbolic Computation with Maple, we can discover lots of (rigorously-proved!) facts about Standard Young Tableaux, in particular the distribution of the entries in any specific cell, and the sorting probabilities.
On Two Related Questions of Wilf Concerning Standard Young Tableaux
本文考虑了 Wilf 提出的与标准杨表相关的两个问题，通过纯组合方法对其中一个问题给出部分解答，并由此对另一问题得出更一般的解答。
We present a new characterization of the shape equivalent class and the Littlewood-Richardson correspondence of Young tableaux in terms of tropical (ultradiscrete) integrable systems. As an application, an alternative proof of the "shape change theorem" is given.
Enumeration of standard Young tableaux of certain truncated shapes
发现并证明了某些截断形状的标准Young tableaux数的意外乘积公式。这些包括偏移的楼梯形状减去东北角的正方形，矩形形状减去东北角的正方形，以及一些变化。
Inversions of Semistandard Young Tableaux
表反转是来自行标准表的同一列的一对条目，它们缺乏使表列标准所需的相对顺序。$i$反演的Young表是具有精确的$i$反演对的行标准表，并且可以被解释为（列标准）Young表的泛化。缺乏重复条目的倒置杨氏表是由弗雷塞引入的，用于计算A型中斯普林格纤维的贝蒂数，后来被比格利和德鲁贝发展为自己的组合对象。本文概括了早期的概念表反转行标准tableaux与重复条目，产生一个有趣的新的概括半标准（而不仅仅是标准）杨tableaux。我们开发了一个闭公式的最大数量的倒置对行标准表具有特定的形状和内容，并证明了$i$倒置表的数量是给定的形状下的内容置换不变。然后，我们列举了各种形状和内容的$i$ -倒置的杨表格，并概括了早期的结果，地方$1$ -倒置的杨表格的一般形状的双射与$0$ -倒置的杨表格的各种相关的形状。
On Descents in Standard Young Tableaux
本文给出了随机标准Young表上下降函数的期望和方差的显式表达式。使用这些，它表明，归一化方差，$V/E^2$，是有界的，当且仅当一定的不等式有关tableau形状的下降函数成立。
Free action and cyclic sieving on skew semi-standard Young tableaux
该研究给出半标准Young表循环筛分现象相关定理的简短证明，并将结果推广到斜形状情形。
Standard Young Tableaux and Colored Motzkin Paths
本文提出了着色Motzkin路的概念，建立了高度有界的$n$ -胞标准Young tableaux（SYT）与长度为$n$的着色Motzkin路之间的一个双射.这一结果不仅给出了标准Young表的格路径解释，而且揭示了至多具有$2d+1$行的SYT集合与至多具有2d行的SYT集合之间的意想不到的内在关系。
We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We also compare our bounds with the existing bounds on the numbers of linear extensions of the corresponding posets.
Quasi-Yamanouchi tableaux are a subset of semistandard Young tableaux and refine standard Young tableaux. They are closely tied to the descent set of standard Young tableaux and were introduced by Assaf and Searles to tighten Gessel's fundamental quasisymmetric expansion of Schur functions. The descent set and descent statistic of standard Young tableaux repeatedly prove themselves useful to consider, and as a result, quasi-Yamanouchi tableaux make appearances in many ways outside of their original purpose. Some examples, which we present in this paper, include the Schur expansion of Jack poly…
Enumeration formulas for Young tableaux in a diagonal strip
我们推导出组合恒等式，涉及伯努利数和欧拉数，为一定的斜形状的标准杨tableaux的数量。这推广了D.安德烈关于上下排列的数量。该分析使用了一个转移算子的方法扩展的方法Elkies，结合一个身份表示的体积的一个舒尔函数的某个多面体。
Standard set-valued Young tableaux are a generalization of standard Young tableaux where cells can contain unordered sets of integers, with the added condition that every integer at position $(i,j)$ must be smaller that every integer at both $(i+1,j)$ and $(i,j+1)$. In this paper, we explore properties of standard set-valued Young tableaux with three rows and a fixed number of integers in every cell of each row (referred to as set-valued tableaux with row-constant density). Our primary focus is on standard set-valued Young tableaux with $1$ integer in each first-row cell, $k-1$ integers in eac…
On the Enumeration of Skew Young Tableaux
本文推广了McKay，Morse和Wilf的工作，给出了在两种情况下斜Young tableaux T的个数的精确公式和渐近公式：（1）T的“内部形状”和胞元总数是固定的，（2）T的内部形状是固定的.证明使用理论的对称函数和估计的不可约字符的对称群由于托马，Vershik，Kerov和Biane。
Standard set-valued Young tableaux are a generalization of standard Young tableaux in which cells may contain more than one integer, with the added conditions that every integer at position $(i,j)$ must be smaller than every integer at positions $(i,j+1)$ and $(i+1,j)$. This paper explores the combinatorics of standard set-valued Young tableaux with two-rows, and how those tableaux may be used to provide new combinatorial interpretations of generalized Catalan numbers. New combinatorial interpretations are provided for the two-parameter Fuss-Catalan numbers (Raney numbers), the rational Catala…
Proof of a Conjecture on Young Tableaux with Walls
本研究证明了关于带墙的三行年轻表格的猜想，并验证了树-儿童网络猜想，解决了系统发育学界长期存在的难题。
Properties of four partial orders on standard Young tableaux
设SYT_n是所有具有n个单元格的标准Young表的集合。在回顾了SYT_n上的弱序、KL序、几何序和链序等四种偏序的定义及其一些重要性质之后，我们证明了三个主要结果：（i）这四种偏序中的任何一种偏序的区间本质上描述了由Poirier和Schottenauer定义的一个霍普夫代数中的乘积。(ii)将tableau发送到其下降集的映射诱导tableaux上所有这些阶的真部与布尔代数2^{[n-1]}的真部的同伦等价。特别地，这些阶在表上的默比乌斯函数是（-1）^{n-3}。(iii)对于四个阶中的两个，可以在具有固定内边界的斜表上定义一个更一般的阶，并类似地分析它们的同伦类型和默比乌斯函数。
Motivated by the study of polytopes formed as the convex hull of permutation matrices and alternating sign matrices, we define several new families of polytopes as convex hulls of sign matrices, which are certain {0,1,-1}-matrices in bijection with semistandard Young tableaux. We investigate various properties of these polytopes, including their inequality descriptions, vertices, facets, and face lattices, as well as connections to alternating sign matrix polytopes and transportation polytopes.
The number of Young Tableaux whose shape is a k by n rectangle is famously (nk)! 0! ... (k-1)!/((n+k-1)!(n+k-2)!... n!) implying that for each specific k, that sequence satisfies a linear recurrence equation with polynomial coefficients of the first order. But what about counting Young tableaux where certain "run lengths" are forbidden? Then things seem to get much more complicated. We conclude with four conjectures and pledge donations to the OEIS in honor of the first provers.
An exceptional equinumerosity of lattice paths and Young tableaux
本文通过构造显式双射，证明Guy、Krattenthaler和Sagan所枚举的平面格路径族与标准杨表集合SYT(n+2,2,1^n)等数。
Enumeration of standard Young tableaux of shifted strips with constant width
令$g_{n_1,n_2}$为截断移位形状的标准杨氏表的数量，其中$n_1$行和每行中的$n_2$框。本文用积分方法分别导出了$g_{3,n}$、$g_{n,4}$和$g_{n,5}$的递推关系式。特别地，$g_{n,4}$是$(2n-1)$-st Pell数。
Lusztig's fake degree is the generating polynomial for the major index of standard Young tableaux of a given shape. Results of Springer and James & Kerber imply that, mysteriously, its evaluation at a $k$-th primitive root of unity yields the number of border strip tableaux with all strips of size $k$, up to sign. This is essentially the special case of the Murnaghan-Nakayama rule for evaluating an irreducible character of the symmetric group at a rectangular partition. We refine this result to standard Young tableaux and border strip tableaux with a given number of descents. To do so, we intr…
An inverted semistandard Young tableau is a row-standard tableau along with a collection of inversion pairs that quantify how far the tableau is from being column semistandard. Such a tableau with precisely $k$ inversion pairs is said to be a $k$-inverted semistandard Young tableau. Building upon earlier work by Fresse and the author, this paper develops generating functions for the numbers of $k$-inverted semistandard Young tableau of various shapes $λ$ and contents $μ$. An easily-calculable generating function is given for the number of $k$-inverted semistandard Young tableau that "standardi…
On the three-rowed skew standard Young tableaux
设$\mathcal{T}_3$为三行条带。最近，Regev指出，在“斜三行带”$\mathcal{T}_3 / (2,1,0)$中，具有$n-3$条目的标准Young表的数量是$m_{n-1}-m_{n-3}$，即两个Motzkin数之差。Zeilberger通过他的强大程序和WZ方法自动推导并严格证明了这个猜想以及数百个类似的恒等式。似乎每一个都是具有常系数的Motzkin数的线性组合。在本文中，我们将介绍一个简单的双射Motzkin路径和标准的扬tableaux最多有三行。有了这个双射，我们肯定地回答了Zeilberger的问题，即有一个统一的方法来构造所有这些恒等式的双射证明。
Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux
本文从组合与动力系统角度研究无限标准杨表上的jeu de taquin操作，分析了其逆像结构，分类了周期、预周期和回归行为，并证明了该操作在Devaney意义下是混沌的。
Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux
你有多少种方法可以把n块不同大小的巧克力放在一个n乘n的巧克力盒子里，当你从左到右，从上到下，没有间隙，每一行每一列的大小都在增加？答案是众所周知的OEIS序列号85。令我们惊讶的是，三维巧克力盒的类似序列并不存在。在这里，我们填补了这一空白，更重要的是，提供了一些计算和理论上的挑战，枚举家庭的固体标准的年轻表。
Random Young Tableaux and Combinatorial Identities
我们导出了新的组合恒等式，它们可以看作是超几何级数求和公式的多元类似物。正如在以前的文件[Re]，我们开始与概率分布的空间上的无限杨tableaux。然后，我们计算在给定的盒子中随机表的条目等于n= 1，2，.的概率。将n上的这些概率求和，并使结果等于1，我们得到一个非平凡的恒等式。我们选择的初始分布的动机是最近的工作调和分析的无限对称群和相关的主题。
Quasi-Yamanouchi tableaux connect the two most studied types of tableaux. They are a subset of semistandard Young tableaux that are also a refinement on standard Young tableaux, and they can be used to improve the fundamental quasisymmetric expansion of Schur polynomials. We prove a product formula for enumerating certain quasi-Yamanouchi tableaux and provide strong evidence that no product formula exists in general for other shapes. Along the way, we also prove some nice properties of their distribution and symmetry.
Humps in Motzkin paths and standard Young tableaux in a $(2,1)$-hook
本文统计给定高度 Motzkin 路径的驼峰与峰，以及前两部分差固定的 $(2,1)$-钩标准 Young 表数量，细化 Regev 的结果并给出新组合证明与递推关系。
Combinatorics of Tableau Inversions
表反转是行标准表$T$中的一对条目，它们位于$T$的同一列中，但缺乏使$T$成为列标准的适当相对顺序。$i$反转的Young工作表是行标准工作表以及精确的$i$反转对。Tableau反演最初由Fresse引入，用于计算A型中Springer纤维的Betti数，其中将$i$反演的tableaux的数量标准化为与相关纤维的特定贝蒂数相对应的固定标准Young Tableau。在本文中，我们从一个完全组合的角度来探讨表反演的问题。我们开发的公式枚举的数量的$i$ -倒置的杨tableaux的各种tableaux形状，不限制自己的倒置tableaux，标准化一个特定的标准杨tableau，并构建双射之间的$i$ -倒置的杨tableaux的某种形状与$j$ -倒置的杨tableaux不同的形状。最后，我们分享一些计算机程序的结果，开发计算tableaux反演。
Pattern avoidance and RSK-like algorithms for alternating permutations and Young tableaux
我们定义了一个类L_{n, k}的置换，推广交替（上下）置换，并给出了双射证明的某些模式，避免此类结果。作为我们结果的一个特例，我们给出了长度为2n且没有四项递增子序列的交替排列集合A_{2n}（1234）与形状为（3 ^n）的标准Young tableaux之间以及集合A_{2n + 1}（1234）与形状为（3^{n - 1}，2，1）的标准Young tableaux之间的两个双射.这表示避免长度为4的模式的交替排列的第一次枚举。我们还扩展以前的工作双交替排列（交替排列的逆交替），我们更一般的情况下。集合L_{n, k}可以被看作是具有特定倾斜形状的标准杨氏表格的阅读单词的集合。在本文的最后一节中，我们扩大了我们的研究，考虑模式避免在阅读的话，标准的杨tableaux的任何歪斜的形状。我们双射表明，标准杨tableaux的形状lambda/mu的阅读单词避免213的数量是一个自然的mu模拟的加泰罗尼亚数字（特别是不依赖于lambda，一个简单的技术条件），并有类似的结果为模式132，231和312。
The hook length formula gives a product formula for the number of standard Young tableaux of a partition shape. The number of standard Young tableaux of a skew shape does not always have a product formula. However, for some special skew shapes, there is a product formula. Recently, Morales, Pak and Panova joint with Krattenthaler conjectured a product formula for the number of standard Young tableaux of shape $λ/μ$ for $λ=((2a+c)^{c+a},(a+c)^a)$ and $μ=(a+1,a^{a-1},1)$. They also conjectured a product formula for the number of standard Young tableaux of a certain skew shifted shape. In this pa…
We consider two examples of a fully decodable combinatorial encoding of Bernoulli schemes: the encoding via Weyl simplices and the much more complicated encoding via the RSK (Robinson--Schensted--Knuth) correspondence. In the first case, the decodability is a quite simple fact, while in the second case, this is a nontrivial result obtained by D.~Romik and P.~Śniady and based on the papers~ \cite{KV}, \cite{VK}, and others. We comment on the proofs from the viewpoint of the theory of measurable partitions; another proof, using representation theory and generalized Schur--Weyl duality, will be p…
Edelman and Greene constructed a bijection between the set of standard Young tableaux and the set of balanced Young tableaux of the same shape. Fomin, Greene, Reiner and Shimozono introduced the notion of balanced Rothe tableaux of a permutation $w$, and established a bijection between the set of balanced Rothe tableaux of $w$ and the set of reduced words of $w$. In this paper, we introduce the notion of standard Rothe tableaux of $w$, which are tableaux obtained by labelling the cells of the Rothe diagram of $w$ such that each row and each column is increasing. We show that the number of stan…
Asymptotics of Young tableaux in the $(k,\ell)$ hook
在~ \cite{berele}中计算“$(k,\ell)$钩状”和$S_{k,\ell}^{(2z)}(n)$（参见~ \eqref{the.sums.1}）的渐近性。人们最近意识到，在~ \cite [第7节]{berele}有一些印刷错误和一定的混乱方面的符号，使精确的渐近$S_{k,\ell}^{(2z)}(n)$是不清楚的。在这里，我们添加更多的细节，并仔细重复这些计算，这导致明确的值的渐近$S_{k,\ell}^{(2z)}(n).$
Realizable Standard Young Tableaux
研究由两个递增向量外和生成的矩形标准杨表（可实现杨表）的渐近计数，证明其数量与总杨表数相比呈指数级稀疏，并给出紧界。
Dyck Paths, Standard Young Tableaux, and Pattern Avoiding Permutations
我们提出了一个生成函数和一个封闭的计数公式在两个变量，列举了一个家庭的类的排列，避免或包含一个增加的模式的长度为3，并有一个规定的次数出现的另一种模式的长度为3。这给出了一些以前研究过的统计数据的改进，其中最著名的是努南的统计数据。该公式还示出了列举一个家庭的类的戴克路径和标准的杨表格，和双射之间的相应的类，这两个家庭的对象。最后，将所得结果用于解决某纸牌游戏的最优化问题。
The study of permutation and partition statistics is a classical topic in enumerative combinatorics. The major index statistic on permutations was introduced a century ago by Percy MacMahon in his seminal works. In this extended abstract, we study the well-known generalization of the major index to standard Young tableaux. We present several new results. In one direction, we introduce and study two partial orders on the standard Young tableaux of a given partition shape, in analogy with the strong and weak Bruhat orders on permutations. The existence of such ranked poset structures allows us t…
We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce a special class of labeled Dyck paths of semilength $n$ that is shown to be in bijection with the set of all SYT with $n$ boxes. In addition, we present bijections from certain classes of Motzkin paths to SYT. As a natural framework for some of our bijections, we introduce a class of set partitions which in some sense is dual to the known class of…
We are interested in the asymptotics of the number of standard Young tableaux $f^{λ/μ}$ of a given skew shape $λ/μ$. We mainly restrict ourselves to the case where both diagrams are balanced, but investigate all growth regimes of $|μ|$ compared to $|λ|$, from $|μ|$ fixed to $|μ|$ of order $|λ|$. When $|μ|=o(|λ|^{1/3})$, we get an asymptotic expansion to any order. When $|μ|=o(|λ|^{1/2})$, we get a sharp upper bound. For bigger $|μ|$, we prove a weaker bound and give a conjecture on what we believe to be the correct order of magnitude. Our results are obtained by expressing $f^{λ/μ}$ in terms o…
Canon permutations and generalized descents of standard Young tableaux
本文将nonnesting排列枚举多项式的分解结果推广至任意k的Canon排列，通过双射证明将其与矩形标准杨表的广义降序枚举相联系，并解决了Sulanke关于格路径统计量分布的猜想。
The distributions of the entries of Young tableaux
设T^* 为k个单元格的标准杨氏表。我们证明，在极限n -> \infty中，一个包含T^* 作为子表的n个单元的杨表的概率等于ν（π（T^*））/k！，其中π（T^*）是T^* 的形状（=费勒斯图），ν（π）是形状为π的所有表格的数量。换句话说，一个大的画面包含T^* 的概率等于T^* 形状的画面的数量除以k！。我们给出了几个应用程序，一组规定的条目将出现在一组规定的单元格的一个画面的概率，并给出的形状subtableaux将发生的概率。我们的论点在于一个概念的拟随机性的家庭的排列，我们给充分条件，这举行。然后，我们扩展这些结果找到一个明确的公式的限制概率，一个年轻的画面有一个给定的一组条目在一组给定的位置。其结果是，一个Young表具有一个规定的条目集k_1，k_2，.，在规定的m个单元的集合中的k_m等于在给定位置具有给定条目的K个单元（K= \max{\{k_i\}}）上的所有表格的测量的总和，其中K个单元的表格的测量是其形状的表格的数量除以K！。在证明中，我们还开发了条件，确保某些家庭的排列的quasirandomness。
On the Young-Fibonacci insertion algorithm
本文研究了Young-Fibonacci插入算法的一些性质及其与Fomin生长图的关系。它还调查了杨-斐波那契tableaux的组合学和冈田的代数与杨-斐波那契格的研究之间的关系。原来的算法介绍了罗比和我们重新定义它在这样一种方式，无论是插入和记录tableaux的任何置换是\emph{conveniently}解释为链的杨斐波纳契格。Killpatrick疏散的一个性质给出了一个更简单的证明，但在使Roby和Fomin的构造重合时不再需要这种疏散。本文给出了大小为$n$的Young-Fibonacci表集的分次偏序集结构，它由对称群置换的弱序诱导，并由表上初等变换的传递闭包实现.我们表明，这个偏序集给出了一个组合的解释的系数在转移阵从模拟的完全对称函数模拟的Schur函数冈田代数。我们结束了一个非常类似的观察四偏序集杨tableaux研究塔斯金。
(Dual-)promotion and (dual-)evacuation are bijections on SYT(λ) for any partition λ. Let c^r denote the rectangular partition (c,...,c) of height r, and let sc_k (k > 2) denote the staircase partition (k,k-1,...,1). B. Rhoades showed representation-theoretically that promotion on SYT(c^r) exhibits the cyclic sieving phenomenon (CSP). In this paper, we demonstrate a promotion- and evacuation-preserving embedding of SYT(sc_k) into SYT(k^{k+1}). This arose from an attempt to demonstrate the CSP of promotion action on SYT(sc_k).
Connections Between Frames with Rational Eigensteps and Semistandard Young Tableaux
本研究建立了有理特征步长框架与半标准杨表的对应关系，提出基于杨表的框架特征步长构造新方法，并用组合技术实现框架补的对应，为框架分析提供组合学新视角。
Bijections for an identity of Young Tableaux
我们提出了一个优雅的双射之间的标准杨tableaux与2n个细胞，最多两行，和对标准杨tableaux相同的形状，与n+1个细胞，只有最上面的一行可以有一个以上的细胞。
We introduce the notions of Schröder shape and of Schröder tableau, which provide some kind of analogs of the classical notions of Young shape and Young tableau. We investigate some properties of the partial order given by containment of Schröder shapes. Then we propose an algorithm which is the natural analog of the well known RS correspondence for Young tableaux, and we characterize those permutations whose insertion tableaux have some special shapes. The last part of the article relates the notion of Schröder tableau with those of interval order and of weak containment (and strong avoidance…
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