Inversion relations, reciprocity and polyominoes
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
1999
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| _version_ | 1866912605277257728 |
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| author | Bousquet-Melou, M. Guttmann, A. J. Orrick, W. P. Rechnitzer, A. |
| author_facet | Bousquet-Melou, M. Guttmann, A. J. Orrick, W. P. Rechnitzer, A. |
| contents | We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase polygons with a staircase hole. In so doing, we establish a connection between the reciprocity results known to combinatorialists and the inversion relations used by physicists to solve models in statistical mechanics. For several classes of convex polygons, the inversion (reciprocity) relation, augmented by certain symmetry and analyticity properties, completely determines the anisotropic perimeter generating function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9908123 |
| institution | arXiv |
| publishDate | 1999 |
| record_format | arxiv |
| spellingShingle | Inversion relations, reciprocity and polyominoes Bousquet-Melou, M. Guttmann, A. J. Orrick, W. P. Rechnitzer, A. Combinatorics 05A15 (Primary) 05B50, 82B20, 82B23 (Secondary) We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase polygons with a staircase hole. In so doing, we establish a connection between the reciprocity results known to combinatorialists and the inversion relations used by physicists to solve models in statistical mechanics. For several classes of convex polygons, the inversion (reciprocity) relation, augmented by certain symmetry and analyticity properties, completely determines the anisotropic perimeter generating function. |
| title | Inversion relations, reciprocity and polyominoes |
| topic | Combinatorics 05A15 (Primary) 05B50, 82B20, 82B23 (Secondary) |
| url | https://arxiv.org/abs/math/9908123 |