Bijective enumeration of rook walks

2020/07/02 by Alexander M. Haupt, Haupt, Alexander M.
Mathematics · #05A19 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A19

paper · pdf · doi:10.48550/arxiv.2007.01018

arxiv created 2020/07/02 · arxiv updated 2020/07/03

Abstract

In this paper we answer a question posed by R. Stanley in his collection of Bijection Proof Problems (Problem 240). We present a bijective proof for the enumeration of walks of length k a chess rook can move along on an m× n board starting and ending on the same square.

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