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An Extremal Problem For Finite Lattices, John Goldwasser, Brendan Nagle, Andres Saez
An Extremal Problem For Finite Lattices, John Goldwasser, Brendan Nagle, Andres Saez
John Copeland Nagle
For a fixed M x N integer lattice L(M,N), we consider the maximum size of a subset A of L(M,N) which contains no squares of prescribed side lengths k(1),...,k(t). We denote this size by ex(L(M,N), {k(1),...,k(t)}), and when t = 1, we abbreviate this parameter to ex(L(M,N), k), where k = k(1).
Our first result gives an exact formula for ex(L( …