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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.03473 |
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| _version_ | 1866910191007563776 |
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| author | Ahlberg, John Alexandersson, Per |
| author_facet | Ahlberg, John Alexandersson, Per |
| contents | We study tilings of rectangular boards using unit squares together with a single type of big tile shaped as a Ferrers diagram.
We derive generating functions for these tilings, prove real-rootedness and interlacing properties of associated independence polynomials, and establish connections with several sequences in the OEIS. Our results touch on tilings involving L-shaped polyominoes, fault-free tilings, and cylindric variants. We prove that tiling polynomials for two-column Ferrers shapes are real-rooted and form interlacing sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03473 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomials from tilings of rectangles Ahlberg, John Alexandersson, Per Combinatorics 05A15, 26C10 We study tilings of rectangular boards using unit squares together with a single type of big tile shaped as a Ferrers diagram. We derive generating functions for these tilings, prove real-rootedness and interlacing properties of associated independence polynomials, and establish connections with several sequences in the OEIS. Our results touch on tilings involving L-shaped polyominoes, fault-free tilings, and cylindric variants. We prove that tiling polynomials for two-column Ferrers shapes are real-rooted and form interlacing sequences. |
| title | Polynomials from tilings of rectangles |
| topic | Combinatorics 05A15, 26C10 |
| url | https://arxiv.org/abs/2605.03473 |