A Step Towards Yuzvinsky's Conjecture

An intercalate matrix M of type [r, s, n] is an r × s matrix with entries in {1, 2, . . . , n} such that all entries in each row are distinct, all entries in each column are distinct, and all 2 × 2 submatrices of M have either 2 or 4 distinct entries. Yuzvinsky’s Conjecture on intercalate matrices claims that the smallest n for which there is an intercalate matrix of type [r, s, n] is the Hopf-Stiefel function r◦s. In this paper we prove Yuzvinsky’s Conjecture is asymptotically true for 56 of integer pairs (r, s). We prove the conjecture for r 6 8, and we study it in the range r, s 6 32.