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Junior Colloquium

An Alternating Sum of Alternating Sign Matrices

Nathan Williams

An alternating-sign matrix (ASM) is a square matrix with entries from {-1, 0,1}, row and column sums of 1, and in which the nonzero entries in each row and column alternate in sign. ASMs have many non-trivial parameters and symmetries that reveal their significant combinatorial structure. In this talk, I'll give a brief history of ASMs and prove an identity that relates one parameter and one symmetry.

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