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Michael Kielstra alternating sign matrices, April 23, 2019

Speaker: Michael Kielstra, April 23, 2019
Title. Snakes and Units: Algorithmic Generation of Alternating Sign Matrices
Abstract. Alternating sign matrices, a generalization of permutation matrices, are fairly simple things: fill a square matrix with 1s, 0s, and -1s, such that each row and column sum to 1 and the signs of the 1s and -1s alternate along each row and column. They're also fairly recent things: we only managed to accurately count them in 1992. I will lay out some of the basic results surrounding these matrices, and describe a novel algorithm for generating them either randomly or sequentially.


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