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 note, we will prove an identity that relates one parameter and one symmetry.

Author Bio

Nathan Williams was introduced to alternating-sign matrices in a class taught by Professor Eric Egge, and was immediately discouraged by the sometimes enormously complicated proofs of even their most basic properties. Nevertheless, he was sufficiently intrigued by their simultaneous accessibility and inaccessibility that he payed enough attention to notice an amusing pattern. Nathan is a recent graduate of Carleton College. This fall he will be starting his Ph.D. in mathematics at the University of Minnesota.