Using Words to Construct and Enumerate Maximum Nonattacking Chessboard Arrangements

Research output: Contribution to book or proceedingConference articlepeer-review

Abstract

Words are ubiquitous objects in combinatorics that can be studied in their own right or be used to represent sets of other combinatorial objects. Additionally, mathematical questions related to chess, its pieces, its board, and the many extensions and generalizations, have been posed for hundreds of years. In particular, chess pieces can have move sets beyond those in the established game of chess. Here we use words to describe nonattacking arrangements of chess pieces on a rectangular 2×2n chessboard. We then extend the notion of words on a single line to a matrix of letters, focusing on pieces who can move with attacks from a king’s move set. Bijections between matrices of letters in small alphabets and nonattacking maximum arrangements of pieces on rectangular chessboards are used to enumerate such arrangements.

Original languageEnglish
Title of host publicationApplied Mathematical Analysis and Computations I - 1st SGMC
EditorsDivine Wanduku, Shijun Zheng, Zhan Chen, Andrew Sills, Haomin Zhou, Ephraim Agyingi
PublisherSpringer
Pages193-223
Number of pages31
ISBN (Print)9783031697050
DOIs
StatePublished - 2024
Event1st Southern Georgia Mathematics Conference, SGMC 2021 - Virtual, Online
Duration: Apr 2 2021Apr 3 2021

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume471
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference1st Southern Georgia Mathematics Conference, SGMC 2021
CityVirtual, Online
Period04/2/2104/3/21

Scopus Subject Areas

  • General Mathematics

Keywords

  • 05A05
  • 05A15
  • Bijection
  • Chess
  • Independence
  • Words

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