Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(5): 1281-1289

Online first article August 25, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150404

Copyright © The Korean Mathematical Society.

Combinatorial enumeration of the regions of some linear arrangements

Seunghyun Seo

Kangwon National University

Abstract

Richard Stanley suggested the problem of finding combinatorial proofs of formulas for counting regions of certain hyperplane arrangements defined by hyperplanes of the form $x_i=0$, $x_i=x_j$, and $x_i=2x_j$ that were found using the finite field method. We give such proofs, using embroidered permutations and linear extensions of posets.

Keywords: hyperplane arrangement, embroidered permutation, linear extensions of poset

MSC numbers: 05A19, 52C35, 06A07

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