# On the Homogenized Linial Arrangement: Intersection Lattice and Genocchi Numbers.

@article{Lazar2018OnTH, title={On the Homogenized Linial Arrangement: Intersection Lattice and Genocchi Numbers.}, author={Alexander Lazar and Michelle L. Wachs}, journal={arXiv: Combinatorics}, year={2018} }

Hetyei recently introduced a hyperplane arrangement (called the homogenized Linial arrangement) and used the finite field method of Athanasiadis to show that its number of regions is a median Genocchi number. These numbers count a class of permutations known as Dumont derangements. Here, we take a different approach, which makes direct use of Zaslavsky's formula relating the intersection lattice of this arrangement to the number of regions. We refine Hetyei's result by obtaining a combinatorial…

## 6 Citations

The Homogenized Linial Arrangement and Genocchi Numbers.

- Mathematics
- 2019

We study the intersection lattice of a hyperplane arrangement recently introduced by Hetyei who showed that the number of regions of the arrangement is a median Genocchi number. Using a different…

Ferrers Graphs, D-Permutations, and Surjective Staircases

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We introduce a new family of hyperplane arrangements inspired by the homogenized Linial arrangement (which was recently introduced by Hetyei), and show that the intersection lattices of these…

C O ] 1 0 A ug 2 02 1 CYCLES OF EVEN-ODD DROP PERMUTATIONS AND CONTINUED FRACTIONS OF GENOCCHI

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Recently, Lazar and Wachs (arXiv:1910.07651) showed that the (median) Genocchi numbers play a fundamental role in the study of the homogenized Linial arrangement and obtained two new permutation…

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We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and web…

Cycles of even-odd drop permutations and continued fractions of Genocchi numbers

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Recently, Lazar and Wachs (arXiv:1910.07651) showed that the (median) Genocchi numbers play a fundamental role in the study of the homogenized Linial arrangement and obtained two new permutation…

Moments of Orthogonal Polynomials and Exponential Generating Functions

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- 2021

Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of (q = 1) classical orthogonal polynomials, and…

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