Schur polynomials, entrywise positivity preservers, and weak majorization

Khare, A and Tao, T (2018) Schur polynomials, entrywise positivity preservers, and weak majorization. In: 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018, 16-20 July 2018, Dartmouth College Hanover; United States.

PDF INT_CON_FOR_POW_SER_ALG_COM_2018.pdf - Published Version Restricted to Registered users only Download (194kB) | Request a copy

Abstract

We prove a monotonicity phenomenon for ratios of Schur polynomials. In this we are motivated by - and apply our result to - understanding polynomials and power series that preserve positive semidefiniteness (psd) when applied entrywise to psd matrices. We then extend these results to classify polynomial preservers of total positivity. As a further application, we extend a conjecture of Cuttler, Greene, and Skandera (2011) to obtain a novel characterization of weak majorization using Schur polynomials. Our proofs proceed through a Schur positivity result of Lam, Postnikov, and Pylyavskyy (2007), and computing the leading terms of Schur polynomials. © FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Item Type:	Conference Paper
Publication:	FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics
Publisher:	Formal Power Series and Algebraic Combinatorics
Additional Information:	cited By 0; Conference of 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 ; Conference Date: 16 July 2018 Through 20 July 2018; Conference Code:161385
Keywords:	Combinatorial mathematics, Leading terms; Monotonicity; Positive semidefiniteness; Power series; Schur polynomials; Total positivity, Polynomials
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	07 Oct 2020 11:13
Last Modified:	07 Oct 2020 11:13
URI:	http://eprints.iisc.ac.in/id/eprint/66399

Actions (login required)

View Item