Vol. 13, No. 5, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17, 1 issue

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
Other MSP Journals
This article is available for purchase or by subscription. See below.
Counting profile strings from rectangular tilings

Anthony Petrosino, Alissa Schembor and Kathryn Haymaker

Vol. 13 (2020), No. 5, 861–870

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 m 2. We describe how profiles arise when enumerating tilings, and we prove that the number of profile strings of length m equals m 3m1 .

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

rectangular tilings, enumeration, induction
Mathematical Subject Classification
Primary: 05A19, 05B45
Received: 4 June 2020
Revised: 16 August 2020
Accepted: 17 August 2020
Published: 5 December 2020

Communicated by Arthur T. Benjamin
Anthony Petrosino
Villanova University
Villanova, PA
United States
Alissa Schembor
Villanova University
Villanova, PA
United States
Kathryn Haymaker
Villanova University
Villanova, PA
United States