V r. 2004 Marcus a Tardos dokázali, že každá čtvercová matice tvaru n krát n s členy 1 a 0, která jako podmatici neobsahuje pevnou permutační matici, má jen O(n) členů rovných 1. Tento výsledek rozšiřujeme na vícerozměrné matice a na hypergrafy. (cs)
In 2004 Marcus and Tardos proved that every n by n matrix that has entries 1 and 0 and avoids a fixed permutation matrix as a submatrix, has only O(n) entries 1. We extend this result to higher dimensional matrices and to hypergraphs.
In 2004 Marcus and Tardos proved that every n by n matrix that has entries 1 and 0 and avoids a fixed permutation matrix as a submatrix, has only O(n) entries 1. We extend this result to higher dimensional matrices and to hypergraphs. (en)