COMBINATORIAL ENUMERATION OF THE REGIONS OF SOME LINEAR ARRANGEMENTS

초록

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(j) = 2x(j) that were found using the finite field method. We give such proofs, using embroidered permutations and linear extensions of posets.

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