What makes a \(\mathbf D_0\) graph Schur positive?
type: Item
instance of: scholarly article
title: What makes a \(\mathbf D_0\) graph Schur positive?
zbMATH Open document ID: 1358.05302
author: Jonah Blasiak
published in: Journal of Algebraic Combinatorics
publication date: 2016-11-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1411.3624
review text: A fundamental problem in the theory of LLT polynomials is to give a positive combinatorial expansion of these polynomials in terms of Schur functions. The paper under review is an attempt to attack this problem by studying \(D_0\) graphs by developing \textit{S. Fomin} and \textit{C. Greene}'s theory of noncommutative Schur functions [Discrete Math. 193, No. 1--3, 179--200 (1998; Zbl 1011.05062)]. In particular, the author constructed a \(D_0\) graph whose generating functions are not Schur positive. The result is surprisingly contrary to the speculation that \(D_0\) graphs always have Schur positive generating functions.
reviewed by: Arthur L. B. Yang
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 6656216
zbMATH Keywords: noncommutative Schur functions
zbMATH Keywords: \(D\) graphs
zbMATH Keywords: Knuth transformations
zbMATH Keywords: dual equivalence graphs
zbMATH Keywords: LLT polynomials
zbMATH Keywords: linear programming
describes a project that uses: Magma
describes a project that uses: Algorithm 457
MaRDI profile type: Publication
OpenAlex ID: W2397733484
arXiv ID: 1411.3624
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DOI: 10.1007/S10801-016-0685-7
description: scientific article; zbMATH DE number 6656216