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.
Seunghyun Seo
Kangwon National University
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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