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arXiv · 2005.06354

$k$-arrangements, statistics and patterns

Shishuo Fu·Guo-Niu Han·Zhicong Lin
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Abstract

The $k$-arrangements are permutations whose fixed points are $k$-colored. We prove enumerative results related to statistics and patterns on $k$-arrangements, confirming several conjectures by Blitvi\'c and Steingr\'imsson. In particular, one of their conjectures regarding the equdistribution of the number of descents over the derangement form and the permutation form of $k$-arrangements is strengthened in two interesting ways. Moreover, as one application of the so-called Decrease Value Theorem, we calculate the generating function for a symmetric pair of Eulerian statistics over permutations arising in our study.

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Shishuo Fu, Guo-Niu Han, Zhicong Lin. 2020-05-13. $k$-arrangements, statistics and patterns. https://arxiv.org/abs/2005.06354

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