Schur-positive sets of permutations via products and grid classes

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• 作者：Sergi Elizalde ; Yuval Roichman
• 关键词：Schur ; positivity ; Permutations ; Descent classes ; Geometric grid classes ; Kronecker product ; Pattern avoidance
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：45
• 期：2
• 页码：363-405
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Convex and Discrete Geometry; Order, Lattices, Ordered Algebraic Structures; Computer Science, general; Group Theory and Generalizations;
• 出版者：Springer US
• ISSN：1572-9192
• 卷排序：45

文摘

Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur-positive is a long-standing problem in algebraic combinatorics. In this paper, we present a general method to construct Schur-positive sets and multisets, based on geometric grid classes and the product operation. Our approach produces many new instances of Schur-positive sets and provides a broad framework that explains the existence of known such sets that until now were sporadic cases.