Decomposition of the product of a monomial and a Demazure atom

We prove that the product of a monomial and a Demazure atom is a positive sum of Demazure atoms combinatorially. This result proves one particular case in a conjecture which provides an approach to a combinatorial proof of Schubert positivity property.

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Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th...
Main Author:	Ying Pun, Anna
Format:	Journal Article Conference Proceeding
Language:	English
Published:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Subjects:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics
ISSN:	1365-8050, 1462-7264, 1365-8050
Online Access:	Get full text
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Description
Summary:	We prove that the product of a monomial and a Demazure atom is a positive sum of Demazure atoms combinatorially. This result proves one particular case in a conjecture which provides an approach to a combinatorial proof of Schubert positivity property.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6323