Colloquium: Curtis Nelson (University of Wyoming)


Event Details


Title: Tiling with dominoes and monomers and an equivalent (0; 1)-matrix existence theorem.

Abstract: Question: Suppose you are given two lists of numbers: R = (r1, r2, …, r7), S = (s1, s2, …, s6). You are then asked to tile a 7 × 6 checkerboard with vertical dominoes (2 × 1 blocks) and monomers (1 × 1 blocks) so that there are exactly  dominoes whose top half is in row i and exactly  dominoes occur in column j. For example, if R = (3, 1, 2, 2,1, 2, 0) and S = (2, 1, 2, 2, 1, 3), a tiling would be:

If R = (1, 2, 2, 2, 2, 3, 0) and S = (3, 1, 3, 1, 1, 3), can you successfully complete the tiling? What about when R = (1, 1, 3, 2, 2, 3, 0) and S = (3, 1, 3, 1, 1, 3)? This question is similar to the question answered by the classical, celebrated result known as the Gale-Ryser Theorem. The answer to the above questions, as well as the answer for the general case, will be given.