The Number of Fillings a 2×2×n prism with 1×1×2 prisms-Reference-Cited by-同舟云学术

The Number of Fillings a 2×2×n prism with 1×1×2 prisms

Published:2023-10-03 Issue: Volume:3 Page:104-114
ISSN:2732-9976
Container-title:EQUATIONS
language:en
Short-container-title:

Author:

Potůček Radovan¹

Affiliation:

1. Department of Mathematics and Physics University of Defence Kounicova 65, 662 10 Brno CZECH REPUBLIC

Abstract

This paper is inspired by very interesting YouTube video of Burkard Polster, professor of mathematics at Monash University in Melbourne, Australia, which, among other things, concerned the number of ways to fill a part of the plane with dominoes, i.e. 1×2 rectangles. First we deal with the numbers of fillings the 2×2×n prism with elementary 1×1×2 prisms for n=1,2,3,4,5. Special symbolism and figures showing the filling of the prism are used as well as the concept of matching from graph theory and the corresponding graph diagrams. Then we generalize these specific considerations and derive a general recurrence formula for any n≥3, which expresses the number of fillings of the 2×2×n prism with 1×1×2 elementary prisms, which in a way can be considered as spatial domino cubes, if we do not consider their marking with pairs of numbers from 0 to 6.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Reference10 articles.

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