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arXiv · 2410.23206

A descent-excedance correspondence in colored permutation groups

Hiranya Kishore Dey·Umesh Shankar·Sivaramakrishnan Sivasubramanian
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Abstract

It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed first letter are identical when we perform a simple change of the first letter. We generalize this to type B and other colored permutation groups. We are led to defining descents and excedances through linear orders. With respect to a particular order, when the number of colors is even, we get a result that generalizes the type B results. Lastly, we get a type B counterpart of Conger's result which refines the well known Carlitz identity.

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Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian. 2024-10-30. A descent-excedance correspondence in colored permutation groups. https://doi.org/10.54550/eca2025v5s3r24

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