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Abstract: We introduce the notion of the descent set polynomial as an alternative wayof encoding the sizes of descent classes of permutations. Descent setpolynomials exhibit interesting factorization patterns. We explore the questionof when particular cyclotomic factors divide these polynomials. As an instancewe deduce that the proportion of odd entries in the descent set statistics inthe symmetric group S n only depends on the number on 1-s in the binaryexpansion of n. We observe similar properties for the signed descent setstatistics.



Author: Denis Chebikin, Richard Ehrenborg, Pavlo Pylyavskyy, Margaret Readdy

Source: https://arxiv.org/







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