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Kohnert polynomials
Sami Assaf,Dominic Searles +1 more
TL;DR: In this paper, Kohnert polynomials stabilize to quasisymmetric functions that are nonnegative on the fundamental basis for quasisysymmetric functions.
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Abstract: We associate a polynomial to any diagram of unit cells in the first quadrant of the plane using Kohnert's algorithm for moving cells down. In this way, for every weak composition one can choose a cell diagram with corresponding row-counts, with each choice giving rise to a combinatorially-defined basis of polynomials. These Kohnert bases provide a simultaneous generalization of Schubert polynomials and Demazure characters for the general linear group. Using the monomial and fundamental slide bases defined earlier by the authors, we show that Kohnert polynomials stabilize to quasisymmetric functions that are nonnegative on the fundamental basis for quasisymmetric functions. For initial applications, we define and study two new Kohnert bases. The elements of one basis are conjecturally Schubert-positive and stabilize to the skew-Schur functions; the elements of the other basis stabilize to a new basis of quasisymmetric functions that contains the Schur functions.
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1991년도 사업경과 보고
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Indecomposable 0-Hecke modules for extended Schur functions
Dominic Searles
- 13 Feb 2020
TL;DR: The extended Schur functions form a basis of quasisymmetric functions that contain the Schur function as mentioned in this paper, which is a representation-theoretic interpretation of this basis by constructing $0$-Hecke modules.
17
$P$-partitions and $p$-positivity
TL;DR: In this paper, the authors derived positivity results for chromatic quasisymmetric functions, unicellular and vertical strip LLT polynomials, multivariate Tutte polynomial and the more general $B$-polynomials.
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Multiplicity-free key polynomials.
Reuven Hodges,Alexander Yong +1 more
TL;DR: The key polynomials, defined by A. Lascoux-M.-P. Schutzenberger, are characters for the Demazure modules of type A as mentioned in this paper.
12
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