Date: Friday, March 30, 2018
Location: 4088 East Hall (4:10 PM to 5:00 PM)
Title: Descent polynomials
Abstract: A permutation pi=pi_1 ... pi_n in the symmetric group S_n has descent set
{i : pi_i > pi_{i+1}}. Given a set I of positive integers and n > max I, the descent polynomial of I is the number of pi in S_n with descent set I.
In 1915, MacMahon proved, using the Principle of Inclusion and Exclusion, that this is a polynomial in n. Amazingly, since then properties of this polynomial do not seem to have been studied at all in the literature. We will investigate the descent polynomial in terms of its degree, coefficients when expanded in a basis of binomial coefficients, and roots. This is joint work with Alexander DiazLopez, Pamela Harris, Erik Insko, and Mohamed Omar.
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Speaker: Bruce Sagan
Institution: Michigan State University
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