4 problems

Let $S$ be an $n\times n$ generalized Latin square, an array with an arbitrary number of symbols in which no symbol appears twice in any row or column. A decomposition into disjoin…

Let $l^{*}(n)$ be the least integer such that every proper edge-coloring of $K_{n,n}$ with at least $l^{*}(n)$ colors can be decomposed into $n$ disjoint multicolored perfect match…

Let $l(n)$ be the least number of symbols that forces a transversal in every generalized Latin square of order $n$ containing at least $l(n)$ symbols. A transversal is a diagonal c…

Let $l(n)$ be the least number of symbols that forces a transversal in every generalized Latin square of order $n$ containing at least $l(n)$ symbols. A transversal is a diagonal w…