Symmetric Domino Tilings of Aztec Diamonds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917823814565888 |
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| author | Paul, Pravakar Saikia, Manjil P. |
| author_facet | Paul, Pravakar Saikia, Manjil P. |
| contents | In this paper, we give inductive sum formulas to calculate the number of diagonally symmetric, and diagonally \& anti-diagonally symmetric domino tilings of Aztec Diamonds. As a byproduct, we also find such a formula for the unrestricted case as well. Our proofs rely on a new technique for counting the number of perfect matchings of graphs, proposed by the authors recently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric Domino Tilings of Aztec Diamonds Paul, Pravakar Saikia, Manjil P. Combinatorics Discrete Mathematics Primary 05C30, Secondary 05A15, 05C70, 52C20, 68R10 In this paper, we give inductive sum formulas to calculate the number of diagonally symmetric, and diagonally \& anti-diagonally symmetric domino tilings of Aztec Diamonds. As a byproduct, we also find such a formula for the unrestricted case as well. Our proofs rely on a new technique for counting the number of perfect matchings of graphs, proposed by the authors recently. |
| title | Symmetric Domino Tilings of Aztec Diamonds |
| topic | Combinatorics Discrete Mathematics Primary 05C30, Secondary 05A15, 05C70, 52C20, 68R10 |
| url | https://arxiv.org/abs/2410.23324 |