A tribute to Dennis Stanton

Mourad E.H. Ismail, Erik Koelink, Victor S Reiner

Research output: Contribution to journalEditorial

Abstract

Some of the research work conducted by Dennis Stanton in the field of algebraic combinatorics and special functions are discussed. His early works include orthogonal polynomials of basic hypergeometric type and relations between several orthogonal polynomials of basic hypergeometric type and finite groups of Lie type. Stanton together with Viennot developed a combinatorial theory for the q-Hermite polynomials and the Askey Wilson integral. Stanton also worked on the Rogers Ramanujan identities giving infinite family of Rogers Ramanujan identities. His combinatorial work includes t-cores and t-quotients of partitions, and the abacus bijection from modular representation theory of the symmetric group. Another persistent theme in Dennis combinatorial work is unimodality and its relation to partially ordered sets.

Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalAdvances in Applied Mathematics
Volume46
Issue number1-4
DOIs
StatePublished - Jan 2011

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Ismail, M. E. H., Koelink, E., & Reiner, V. S. (2011). A tribute to Dennis Stanton. Advances in Applied Mathematics, 46(1-4), 1-14. https://doi.org/10.1016/j.aam.2010.09.005