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arXiv · 2505.15664

$q$-analogues of Fisher's inequality and oddtown theorem

Hiranya Kishore Dey
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Abstract

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.

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Hiranya Kishore Dey. 2025-05-21. $q$-analogues of Fisher's inequality and oddtown theorem. https://doi.org/10.1016/j.laa.2026.03.032

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