Connecting peak and descent polynomials

Algebraic and Enumerative Combinatorics

16 January 10:00 - 10:50

Ezgi Kantarci Oguz - KTH Royal Institute of Technology

Denote by $d(S,n)$ the number of permutations of $n$ with a given descent set $S$. This is a polynomial in $n$, called the descent polynomial. An analogous construction for the peak statistic, adjusted by a power of $2$ gives us the peak polynomial $p(I,n)$. In this talk, we tie the theory of peak and descent polynomials together by giving a binary expansion of $d(S,n)$ in terms of peak polynomials. We then define involutions on permutations that give a combinatorial interpretation for the coefficients of $p(I,n)$ in a binomial basis centered at $\mathrm{max}(I)$. The seminar will take place in Kuskvillan Seminar Hall.
Sara Billey
University of Washington
Petter Brändén
KTH Royal Institute of Technology
Sylvie Corteel
Université Paris Diderot, Paris 7
Svante Linusson
KTH Royal Institute of Technology


Svante Linusson


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