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2020 Counting profile strings from rectangular tilings
Anthony Petrosino, Alissa Schembor, Kathryn Haymaker
Involve 13(5): 861-870 (2020). DOI: 10.2140/involve.2020.13.861

Abstract

We study the enumeration of profiles, which are outlines that occur when tiling a rectangular board with squares, dominoes, and trominoes. Profiles of length m correspond to a special subset of the set {0,1,2,3}m, called profile strings. Profiles and their corresponding strings first appeared in the enumeration of the tilings of rectangular 2×n and 3×n boards with squares, dominoes, and trominoes. Profiles also play a role in enumerating the tilings of an m×n board for any fixed m2. We describe how profiles arise when enumerating tilings, and we prove that the number of profile strings of length m equals m3m1.

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Anthony Petrosino. Alissa Schembor. Kathryn Haymaker. "Counting profile strings from rectangular tilings." Involve 13 (5) 861 - 870, 2020. https://doi.org/10.2140/involve.2020.13.861

Information

Received: 4 June 2020; Revised: 16 August 2020; Accepted: 17 August 2020; Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4190443
Digital Object Identifier: 10.2140/involve.2020.13.861

Subjects:
Primary: 05A19, 05B45

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 5 • 2020
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