Cross t-Intersecting Integer Sequences from Weighted Erdős-Ko-Rado

Let m,n and t be positive integers. Consider [m] as the set of sequences of length n on anm-letter alphabet. We say that two subsets A ⊂ [m] and B ⊂ [m] cross t-intersect if any two sequences a ∈ A and b ∈ B match in at least t positions. In this case it is shown that if m > (1− 1 t 2 ) −1 then |A||B| ≤ (mn−t)2. We derive this result from a weighted version of the Erdős–Ko–Rado theorem concerning cross t-intersecting families of subsets, and we also include the corresponding stability statement. One of our main tools is the eigenvalue method for intersection matrices due to Friedgut [10]. (2010 AMS subject classification codes 05D05, 05C50.)

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