@inproceedings{10b0ea99cb6747e99f3bc398efda3b7e,
title = "Using Words to Construct and Enumerate Maximum Nonattacking Chessboard Arrangements",
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{\textquoteright}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.",
keywords = "05A05, 05A15, Bijection, Chess, Independence, Words",
author = "Brown, {Tricia Muldoon}",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 1st Southern Georgia Mathematics Conference, SGMC 2021 ; Conference date: 02-04-2021 Through 03-04-2021",
year = "2024",
doi = "10.1007/978-3-031-69706-7_8",
language = "English",
isbn = "9783031697050",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "193--223",
editor = "Divine Wanduku and Shijun Zheng and Zhan Chen and Andrew Sills and Haomin Zhou and Ephraim Agyingi",
booktitle = "Applied Mathematical Analysis and Computations I - 1st SGMC",
address = "Germany",
}