首页/论文/math/0206045

arXiv math/02060452002-06-05math.CO

Generalization of Schensted insertion algorithm to the cases of hooks and semi-shuffles

Mikhail Kogan

备注：: 22 pages

英文摘要：

Given an rc-graph $R$ of permutation $w$ and an rc-graph $Y$ of permutation $v$, we provide an insertion algorithm, which defines an rc-graph $R\leftarrow Y$ in the case when $v$ is a shuffle with the descent at $r$ and $w$ has no descents greater than $r$ or in the case when $v$ is a shuffle, whose shape is a hook. This algorithm gives a combinatorial rule for computing the generalized Littlewood-Richardson coefficients $c^{u}_{wv}$ in the two cases mentioned above.

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。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

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

相关论文

Quasisymmetric (k,l)-hook Schur functions

We introduce a quasisymmetric generalization of Berele and Regev's hook Schur functions and prove that these new quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. We examine the combinatorics of the quasisymmetric hook Schur functions, providing a relationship to Gessel's fundamental quasisymmetric functions and an analogue of the Robinson-Schensted-Knuth algorithm. We also prove that the multiplication of quasisymmetric hook Schur functions with hook Schur functions behaves the same as the multiplication of quasisymmetric Schur functions with Schur funct…

2016-06-22math.CO

具有指定罗宾逊-斯chensted形状的排列的显式边缘分布

Explicit marginal distributions for permutations with prescribed Robinson-Schensted shape

本文研究了给定形状对排列局部行为的控制，推导了特定形状下σ(i)=j的概率公式，并分析了矩阵中的复杂衍射模式，发现当形状最大部分趋于无穷时，固定点比例趋近于Wallis积分。

2026-05-11math.CO

钩型Schur多重zeta值的洗牌乘积公式

Shuffle product formula of the Schur multiple zeta values of hook type

Sophia University（上智大学）；Tokyo University of Science（东京理科大学）

该研究聚焦钩型Schur多重zeta值的洗牌乘积，通过定义2-标记Schur偏序集推广相关积分表达式，引入初等阶乘Schur多重zeta函数并推广偏序集，最终得到其洗牌乘积的显式公式。

2022-01-11math.COmath.NT

Shuffle Invariance of the Super-RSK Algorithm

As in the $(k,l)$-RSK (Robinson-Schensted-Knuth) of [1], other super-RSK algorithms can be applied to sequences of variables from the set $\{t_1,...,t_k,u_1,...,u_l\}$, where $t_1<...<t_k$, and $u_1<...<u_l$. While the $(k,l)$-RSK of [1] is the case where $t_i<u_j$ for all $i$ and $j$, these other super-RSK's correspond to all the $(\big{(}{{k+l}\atop{k}}\big{)}$ shuffles of the $t$'s and $u$'s satisfying the above restrictions that $t_1<...<t_k$ and $u_1<...<u_l$. We show that the shape of the tableaux produced by any such super-RSK is independent of the particular shuffle of the $t$'s and $u…

2001-03-29math.CO

Descent sets on 321-avoiding involutions and hook decompositions of partitions

We show that the distribution of the major index over the set of involutions in S_n that avoid the pattern 321 is given by the q-analogue of the n-th central binomial coefficient. The proof consists of a composition of three non-trivial bijections, one being the Robinson-Schensted correspondence, ultimately mapping those involutions with major index m into partitions of m whose Young diagram fits inside an n/2 by n/2 box. We also obtain a refinement that keeps track of the descent set, and we deduce an analogous result for the comajor index of 123-avoiding involutions.

2014-07-24math.CO

A combinatorial model for $\nabla m_μ$

The modified Macdonald polynomials introduced by Garsia and Haiman (1996) have many remarkable combinatorial properties. One such class of properties involves applying the $\nabla$ operator of Bergeron and Garsia (1999) to basic symmetric functions. The first discovery of this type was the Shuffle Conjecture of Haglund, Haiman, Loehr, Remmel, and Ulyanov (2005), which relates the expression $\nabla e_n$ to parking functions. A refinement of this conjecture, called the Compositional Shuffle Conjecture, was introduced by Haglund, Morse, and Zabrocki (2012) and proved by Carlsson and Mellit (2015…

2018-04-17math.CO

更多相关论文收起更多论文

Greene--Kleitman invariants for Sulzgruber insertion

R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets of rim-hooks of the same partition shape. It is known that Hillman-Grassl may be equivalently defined using the Robinson-Schensted-Knuth correspondence, and we show the analogous result for Sulzgruber's insertion. We refer to our description of Sulzgruber's insertion as diagonal RSK. As a consequence of this equivalence, we show that Sulzgruber's map from multisets of rim hooks to reverse plane partitions can be expre…

2017-08-31math.CO

RSK 到 d-完全偏序集的推广

A generalization of RSK to $d$-complete posets

本文通过定义 Robinson-Schensted-Knuth 双射在 d-完全偏序集上的推广，给出了 d-完全偏序集钩长公式的一个初等纯组合新证明。

2025-08-21math.CO

Shape Avoiding Permutations

Permutations avoiding all patterns of a given shape (in the sense of Robinson-Schensted-Knuth) are considered. We show that the shapes of all such permutations are contained in a suitable thick hook, and deduce an exponential growth rate for their number.

2001-03-23math.CO

Applications of Symmetric Functions to Cycle and Subsequence Structure after Shuffles

Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after various shuffling methods, emphasizing the role of Cauchy type identities and the Robinson-Schensted-Knuth correspondence. One consequence is a cycle index for riffle shuffles when one deals from the bottom of the deck; conclusions are drawn concerning the distribution of fixed points and the asymptotic distribution of cycle structure. In studying cycle structure of unimodal permutations and their generalizations we are led to an interesting variation of the RSK corresponden…

2002-01-29math.COmath.PR

Burge对应与晶体图

The Burge correspondence and crystal graphs

本文利用Burge阵列的峰谷条件刻画钩形简单图，并为其构造晶体结构，其极值向量对应度序列为阈值且钩形的简单图，为推广Schensted关于RSK插入的结果迈出第一步。

2022-11-01math.CO

Kronecker coefficients for one hook shape

We give a positive combinatorial formula for the Kronecker coefficient g_{lambda mu(d) nu} for any partitions lambda, nu of n and hook shape mu(d) := (n-d,1^d). Our main tool is Haiman's \emph{mixed insertion}. This is a generalization of Schensted insertion to \emph{colored words}, words in the alphabet of barred letters \bar{1},\bar{2},... and unbarred letters 1,2,.... We define the set of \emph{colored Yamanouchi tableaux of content lambda and total color d} (CYT_{lambda, d}) to be the set of mixed insertion tableaux of colored words w with exactly d barred letters and such that w^{blft} is…

2012-09-10math.COmath.RT

Schur Function Expansions and the Rational Shuffle Theorem

Gorsky and Negut introduced operators $Q_{m,n}$ on symmetric functions and conjectured that, in the case where $m$ and $n$ are relatively prime, the expression ${Q}_{m,n}(1)$ is given by the Hikita polynomial ${H}_{m,n}[X;q,t]$. Later, Bergeron-Garsia-Leven-Xin extended and refined the conjectures of ${Q}_{m,n}(1)$ for arbitrary $m$ and $n$ which we call the Extended Rational Shuffle Conjecture. In the special case ${Q}_{n+1,n}(1)$, the Rational Shuffle Conjecture becomes the Shuffle Conjecture of Haglund-Haiman-Loehr-Remmel-Ulyanov, which was proved in 2015 by Carlsson and Mellit as the Shuff…

2020-04-13math.CO