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arXiv · 1912.08551

Width-k Eulerian polynomials of type A and B and its Gamma-positivity

Marwa Ben Abdelmaksoud·Adel Hamdi
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Abstract

We define some generalizations of the classical descent and inversion statistics on signed permutations that arise from the work of Sack and Ulfarsson [20] and called after width-k descents and width-k inversionsof type A in Davis's work [8]. Using the aforementioned new statistics, we derive some new generalizations of Eulerian polynomials of type A, B and D. It should also be noticed that we establish the Gamma-positivity of the "width-k" Eulerian polynomials and we give a combinatorial interpretation of finite sequences associated to these new polynomials using quasisymmetric functions and P-partition in Petersen's work [18].

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Marwa Ben Abdelmaksoud, Adel Hamdi. 2019-12-18. Width-k Eulerian polynomials of type A and B and its Gamma-positivity. https://arxiv.org/abs/1912.08551

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