Mathematics Seminar
Date: Tuesday, 27 February 2024
Time: 10.30 AM
Venue: Lecture Hall 4
Coefficientwise Hankel-total positivity of the Schett polynomials
Bishal Deb
Université Paris Cité, CNRS, Paris.
27-02-24

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Abstract

A half-century ago, Schett (1976) implicitly and then Dumont (1979) explicitly introduced a sequence of polynomials in three variables which unify and generalize the Taylor coefficients of the Jacobian elliptic functions sn, cn and dn. Dumont provided combinatorial interpretations for these polynomials as permutation statistics. We will begin this talk by introducing these polynomials. We will then state some results from the theory of coefficientwise total positivity for Hankel matrices. Finally, we will state and (if time permits) sketch the proof of our main result where we show that the even and odd subsequences of the Schett polynomials are coefficientwise Hankel-totally positive.

This talk will be based on joint work with Alan Sokal.