On combinatorial generalization(s) of Borel transform: Averaging method in combinatorics of symmetric polynomials

On combinatorial generalization(s) of Borel transform: Averaging method in combinatorics of symmetric polynomials

We elaborate on the recent suggestion to consider averaging of Cauchy identities for the Schur functions over power sum variables. This procedure has apparent parallels with the Borel transform, only it changes the number of combinatorial factors like dR in the sums over Young diagrams instead of ju...

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Bibliographic Details
Published in:Physics letters. B Vol. 843; p. 138037
Main Authors: Mironov, A., Morozov, A.
Format: Journal Article
Language:English
Published: Elsevier B.V 10-08-2023
Elsevier
Online Access:Get full text
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Summary:We elaborate on the recent suggestion to consider averaging of Cauchy identities for the Schur functions over power sum variables. This procedure has apparent parallels with the Borel transform, only it changes the number of combinatorial factors like dR in the sums over Young diagrams instead of just factorials in ordinary sums over numbers. It provides a universal view on a number of previously known, but seemingly random identities.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2023.138037