Insertion Algorithms for Gelfand $$S_n$$ -Graphs

IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED
Eric Marberg, Yifeng Zhang
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引用次数: 0

Abstract

The two tableaux assigned by the Robinson–Schensted correspondence are equal if and only if the input permutation is an involution, so the RS algorithm restricts to a bijection between involutions in the symmetric group and standard tableaux. Beissinger found a concise way of formulating this restricted map, which involves adding an extra cell at the end of a row after a Schensted insertion process. We show that by changing this algorithm slightly to add cells at the end of columns rather than rows, one obtains a different bijection from involutions to standard tableaux. Both maps have an interesting connection to representation theory. Specifically, our insertion algorithms classify the molecules (and conjecturally the cells) in the pair of W-graphs associated with the unique equivalence class of perfect models for a generic symmetric group.

Abstract Image

格尔凡$S_n$$图的插入算法
当且仅当输入的排列是一个卷积时,由罗宾逊-申斯特对应关系分配的两个表元是相等的,因此 RS 算法限制了对称群中的卷积与标准表元之间的双射。贝辛格找到了一种简洁的方法来表述这种受限映射,即在申斯泰德插入过程之后,在行尾添加一个额外的单元格。我们的研究表明,只要稍微改变一下这种算法,在列末而不是行末添加单元格,就能得到从渐开线到标准表法的不同偏射。这两种映射都与表示理论有着有趣的联系。具体地说,我们的插入算法对与一般对称群完美模型的唯一等价类相关联的一对 W 图中的分子(以及猜想中的单元格)进行了分类。
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来源期刊
Annals of Combinatorics
Annals of Combinatorics 数学-应用数学
CiteScore
1.00
自引率
0.00%
发文量
56
审稿时长
>12 weeks
期刊介绍: Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches
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