Enumeration of Tableaux of Unusual Shapes

TL;DR

This paper develops a method using generalized hypergeometric functions to enumerate standard Young tableaux of battery shapes, providing a solution to a specific chess problem involving permutation enumeration.

Contribution

It introduces a novel enumeration technique for SYT of battery shapes, expanding combinatorial methods applied to chess-related permutation problems.

Findings

Enumeration of SYT of battery shapes achieved

Solution to Buchanan's chess problem provided

Application of hypergeometric functions in combinatorics demonstrated

Abstract

In this thesis we enumerate standard young tableaux (SYT) of certain truncated skew shapes, which we call battery shapes. This is motivated by a chess problem. In an enumerative chess problem, the set of moves in the solution is (usually) unique, but the order is not. The task of counting the feasible permutations may be accomplished by solving an equivalent problem in enumerative combinatorics. Almost all such problems have been of a special type known as series movers. In this thesis we use generalized hypergeometric functions to enumerate SYT of battery shapes, and thus solve a chess problem posed by Buchanan.