q-analogues of Fisher's inequality and oddtown theorem

2025/05/21 by Dey, Hiranya Kishore
#05A30 #05D05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.15664

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.

Citations

• Modular and fractional L-intersecting families of vector spaces
• A combinatorial proof of Fisher's Inequality
• INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

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