Straight polyomino tilings of rectangles and special rim-hook tableaux
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911618745499648 |
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| author | Aggarwal, Mudit Koley, Hrishik Ram, Samrith |
| author_facet | Aggarwal, Mudit Koley, Hrishik Ram, Samrith |
| contents | We derive explicit rational generating functions for weighted tilings of $2k\times n$ rectangles by straight $k\times 1$ tiles. Our approach combines a decomposition by fault lines with a Hadamard-product framework. Tools from algebraic combinatorics are used together with a theorem of Klivans and Reiner on Schur expansions of plethystic compositions of elementary symmetric functions. This translates the tiling problem into a combinatorial framework via special rim-hook tableaux. On the tiling side, Graham's theorem on fault-free tilings provides the key input needed to complete the analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21852 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Straight polyomino tilings of rectangles and special rim-hook tableaux Aggarwal, Mudit Koley, Hrishik Ram, Samrith Combinatorics 05A15, 05B45, 05E05, 15A15 We derive explicit rational generating functions for weighted tilings of $2k\times n$ rectangles by straight $k\times 1$ tiles. Our approach combines a decomposition by fault lines with a Hadamard-product framework. Tools from algebraic combinatorics are used together with a theorem of Klivans and Reiner on Schur expansions of plethystic compositions of elementary symmetric functions. This translates the tiling problem into a combinatorial framework via special rim-hook tableaux. On the tiling side, Graham's theorem on fault-free tilings provides the key input needed to complete the analysis. |
| title | Straight polyomino tilings of rectangles and special rim-hook tableaux |
| topic | Combinatorics 05A15, 05B45, 05E05, 15A15 |
| url | https://arxiv.org/abs/2604.21852 |