On two-toned tilings and $(m,n)$-words

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This is a Quantitative Study study.

Henri Mühle

doi:10.48550/arxiv.2510.00226

September 30, 2025Open Access

On two-toned tilings and $(m,n)$-words

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Key Points

A clear bijection connects two-toned tilings with (m,n)-words, enhancing understanding of their structure.
The work involves defining two-toned tilings and exploring their properties with respect to (m,n)-words.
The methodology allows for precise analysis of the relation, employing combinatorial techniques.
Understanding this bijection may have implications in combinatorial designs and operations research.

Implication

This article reveals a bijection between two-toned tilings and (m,n)-words, suggesting a new perspective on their relationship.

Abstract

In this article, we describe an explicit bijection between the set of $(m,n)$-words as defined by Pilaud and Poliakova and the set of of two-toned tilings of a strip of length $m+n$.

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Cite This Study

Henri Mühle (2025) studied this question.

synapsesocial.com/papers/68e24e6fd6d66a53c2473e11 https://doi.org/10.48550/arxiv.2510.00226

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On two-toned tilings and $(m,n)$-words

Key Points

Implication

Abstract

Discussion

Cite This Study

On two-toned tilings and $(m,n)$-words

Key Points

Implication

Abstract

Discussion

Cite This Study

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