$q$-analogues of Fisher's inequality and oddtown theorem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911577666486272 |
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| author | Dey, Hiranya Kishore |
| author_facet | Dey, Hiranya Kishore |
| contents | A classical result in design theory, known as Fisher's inequality, states that if every pair of clubs in a town shares the same number of members, then the number of clubs cannot exceed the number of inhabitants in the town. In this short note, we establish a $q$-analogue of Fisher's inequality. Additionally, we present a $q$-analogue of the oddtown theorem for the case when $q$ is an odd prime power. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $q$-analogues of Fisher's inequality and oddtown theorem Dey, Hiranya Kishore Combinatorics 05D05, 05A30 A classical result in design theory, known as Fisher's inequality, states that if every pair of clubs in a town shares the same number of members, then the number of clubs cannot exceed the number of inhabitants in the town. In this short note, we establish a $q$-analogue of Fisher's inequality. Additionally, we present a $q$-analogue of the oddtown theorem for the case when $q$ is an odd prime power. |
| title | $q$-analogues of Fisher's inequality and oddtown theorem |
| topic | Combinatorics 05D05, 05A30 |
| url | https://arxiv.org/abs/2505.15664 |