Jacobian elliptic functions and a family of bivariate peak polynomials
type: Item
instance of: scholarly article
title: Jacobian elliptic functions and a family of bivariate peak polynomials
zbMATH Open document ID: 1473.33010
author: Shi-Mei Ma
author: Jun Ma
author: Yeong-Nan Yeh
author: Roberta Rui Zhou
published in: European Journal of Combinatorics
publication date: 2021-08-05T00:00:00Z
review text: This paper has several combinatorial aims. After a long introduction with Taylor expansions of Jacobi elliptic functions, a combinatorial expansion for a family of bivariate peak polynomials, which count permutations by their odd and even cycle peaks, is given. This combinatorial expansion implies that the coefficient polynomials of sn\((u , k)\) are \(\gamma\)-positive. Furthermore, the coefficient polynomials of cn\((u , k)\) are bi-\(\gamma\)-positive. Then combinatorial interpretations of some numbers in terms of increasing trees are presented. Finally, combinatorial interpretations of two associated coefficients in terms of increasing trees are found. The proofs use the derivative operator acting on commuting variables, context-free grammar, grammatical labeling and induction.
reviewed by: Thomas Ernst
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 7379248
zbMATH Keywords: Jacobi elliptic function
zbMATH Keywords: grammatical labeling
zbMATH Keywords: context-free grammar
zbMATH Keywords: \(\gamma\)-positive
zbMATH Keywords: combinatorial interpretation
MaRDI profile type: Publication
full work available at URL: j.ejc.2021.103371
OpenAlex ID: W3165915101
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DOI: 10.1016/J.EJC.2021.103371
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description: scientific article; zbMATH DE number 7379248