Characteristic polynomial of the hyperplane arrangements $\mathcal J_n$ via finite field method

Joungmin Song

doi:10.4134/CKMS.c170323

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2018; 33(3): 759-765

Online first article June 25, 2018 Printed July 1, 2018

https://doi.org/10.4134/CKMS.c170323

Characteristic polynomial of the hyperplane arrangements $\mathcal J_n$ via finite field method

Joungmin Song

GIST

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Abstract

We use the finite method developed by C. Athanasiadis based on Crapo-Rota's theorem to give a complete formula for the characteristic polynomial of hyperplane arrangements $\mathcal J_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $ 1\leq i, j, k, l\leq n$.

Keywords: hyperplane arrangements, finite field method

MSC numbers: Primary 32S22, 05C30