# The Homogenized Linial Arrangement and Genocchi Numbers.

@article{Lazar2019TheHL, title={The Homogenized Linial Arrangement and Genocchi Numbers.}, author={Alexander Lazar and Michelle L. Wachs}, journal={arXiv: Combinatorics}, year={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 method, we refine Hetyei's result by providing a combinatorial interpretation of the coefficients of the characteristic polynomial of the intersection lattice of this arrangement. We also show that the Mobius invariant of the intersection lattice is a (nonmedian) Genocchi number. The Genocchi numbers…

## 5 Citations

Ferrers Graphs, D-Permutations, and Surjective Staircases

- Mathematics
- 2021

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…

Gamma-positivity for a Refinement of Median Genocchi Numbers

- Mathematics
- 2021

We study the generating function of descent numbers for the permutations with descent pairs of prescribed parities, the distribution of which turns out to be a refinement of median Genocchi numbers.…

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

- 2021

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…

Parity considerations for drops in cycles on $\{1,2,\ldots,n\}$

- Mathematics
- 2021

In 2019, A. Lazar and M. L. Wachs conjectured that the number of cycles on [2n] with only even-odd drops equals the n-th Genocchi number. In this paper, we restrict our attention to a subset of…

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

- Mathematics
- 2021

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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