-analogues of Fisher's inequality and oddtown theorem
arXiv:2505.15664 · doi:10.1016/j.laa.2026.03.032
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 -analogue of Fisher's inequality. Additionally, we present a -analogue of the oddtown theorem for the case when is an odd prime power.
9 pages, Comments and suggestions are welcome