The descent set polynomial revisited

Abstract

We continue to explore cyclotomic factors in the descent set polynomial $Q_n(t)$, which was introduced by Chebikin, Ehrenborg, Pylyavskyy and Readdy. We obtain large classes of factors of the form ${\Phi }_{2s}$ or ${\Phi }_{4s}$ where $s$ is an odd integer, with many of these being of the form ${\Phi }_{2p}$ where $p$ is a prime. We also show that if ${\Phi }_2$ is a factor of $Q_{2n}(t)$ then it is a double factor. Finally, we give conditions for an odd prime power $q=p^r$ for which ${\Phi }_{2p}$ is a double factor of $Q_{2q}(t)$ and of $Q_{q+1}(t)$.

26 pages, 6 tables and 1 figure. Results improved to non-prime cyclotomic factors

Cited by in corpus (1)

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