2012
DOI: 10.48550/arxiv.1210.3799
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Some remarks on the joint distribution of descents and inverse descents

Abstract: We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative integer coefficients. We investigate the action of the Eulerian operators that give the recurrence for these generating functions. As a result we devise a recurrence for the coefficients in question but are unable to settle the conjecture.We examine generalizations of the co… Show more

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