Affine and combinatorial binary m-spaces
Let V(n) denote the n-dimensional vector space over GF(2). Let a(m,r) (respectively, c(m,r)) denote the smallest positive integer such that if \(n\geq a(m,r)\) (respectively, \(n\geq c(m,r))\), and V(n) is arbitrarily partitioned into r classes \(C_ i\), \(1\leq i\leq r\), then some class \(C_ i\) must contain an m-dimensional affine (respectively, combinatorial) subspace of V(n). The author investigates upper bounds for the functions a(m,r) and c(m,r) and for the corresponding ''density functions'' \(\bar a(\)m,\(\epsilon)\) and \(\bar c(\)m,\(\epsilon)\).
scientific article; zbMATH DE number 3915093