Regular structures of an intractable enumeration problem: a diagonal recurrence relation of monomer-polymer coverings on two-dimensional rectangular lattices Article Swipe

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Yong Kong ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2411.04147

The enumeration of polymer coverings on two-dimensional rectangular lattices is considered as "intractable". We prove that the number of coverings of $s$ polymer satisfies a simple recurrence relation $ \sum_{i=0}^{2s} (-1)^i \binom{2s}{i} a_{n-i, m-i} = 2^s {(2s)!} / {s!} $ on a $n \times m$ rectangular lattice with open boundary conditions in both directions.

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Enumeration Diagonal Recurrence relation Relation (database) Mathematics Monomer Combinatorics Polymer Materials science Geometry Computer science Data mining Composite material

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2411.04147
PDF: https://arxiv.org/pdf/2411.04147
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Related Works: 10
OpenAlex ID: https://openalex.org/W4404404583

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DOI: https://doi.org/10.48550/arxiv.2411.04147

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Title: Regular structures of an intractable enumeration problem: a diagonal recurrence relation of monomer-polymer coverings on two-dimensional rectangular lattices

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-11-05

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Authors: Yong Kong

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Landing page: https://arxiv.org/abs/2411.04147

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Concepts: Enumeration, Diagonal, Recurrence relation, Relation (database), Mathematics, Monomer, Combinatorics, Polymer, Materials science, Geometry, Computer science, Data mining, Composite material

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