Alternating Sign Matrices and Beyond, Part II

Jim Propp

University of Wisconsin

March 3,
refreshments at 3:45pm


The solution of the alternating sign matrix problem by Zeilberger is likely to be only the end of the first chapter of a very long and interesting story. In the first part of this talk I discussed symmetry classes of ASMs and halved ASMs. I also discussed conjectured enumerations that arise from viewing ASMs as states in a densely-packed loop model.

Yet another chapter-in-the-making of the ASM story concerns the matrix condensation process, due to Dodgson, that inspired Mills, Robbins, and Rumsey to invent ASMs in the first place. Variant forms of condensation give rise to new analogues of ASMs that are enumerated by Somos sequences. These curious integer sequences were originally introduced by Michael Somos in connection with the theory of elliptic functions.

NOTE: despite the title, this talk will be entirely self-contained and will not depend in any way on the first part (given last semester).

Speaker's Contact Info: propp(at-sign)

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