English

Bijective enumeration of rook walks

Combinatorics 2020-07-03 v1

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 kk a chess rook can move along on an m×nm\times n board starting and ending on the same square.

Cite

@article{arxiv.2007.01018,
  title  = {Bijective enumeration of rook walks},
  author = {Alexander M. Haupt},
  journal= {arXiv preprint arXiv:2007.01018},
  year   = {2020}
}
R2 v1 2026-06-23T16:47:48.710Z