Enumeration of Some Closed Knight Paths
Stoyan Kapralov, Valentin Bakoev, Kaloyan Kapralov
TL;DR
This paper systematically enumerates and classifies all closed knight paths of lengths 4, 6, and 8 on a square board of size n+1, revealing the exact number of equivalence classes for each length.
Contribution
It provides a complete enumeration and classification of closed knight paths of specific lengths, a novel combinatorial analysis in chess path enumeration.
Findings
3 equivalence classes of length 4
25 equivalence classes of length 6
478 equivalence classes of length 8
Abstract
The aim of the paper is to enumerate all closed knight paths of length n over a square board of size n+1. The closed knight paths of length 4, 6 and 8 are classified up to equivalence. We determine that there are exactly 3 equivalence classes of closed knight paths of length 4, exactly 25 equivalence classes of closed knight paths of length 6 and exactly 478 equivalence classes of closed knight paths of length 8.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics