Hassan Izanloo (Combinatorics)

29-01-2021 at 2pm to 3pm

Location: Blackboard collaborate: use the signup link to join

Audience: Public

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Title: The enumeration of higher spin alternating sign matrices.


Abstract:

An alternating sign matrix of order n, or an ASM for short, is an n by n matrix with entries from {-1,0,1} such that all row and column sums equal 1 and along each row and column the non-zero entries alternate in sign. The set of all ASMs of order n is denoted by ASM(n). They were first introduced by Bill Mills, Dave Robbins and Howard Rumsey in 1982. It turns out that the ASMs have many faces and that have connections with many other combinatorial objects such as plane partitions, six-vertex configurations and so forth. In this talk I will discuss some new results regarding the enumeration of higher spin ASMs by constructing an explicit bijection between higher spin ASMs and a disjoint union of sets of certain (P,W)-partitions (where P is a certain partially ordered set and W is a labelling). Higher spin ASMs are natural generalizations of ASMs introduced by Behrend and Knight (They are n by n matrices with integer entries such that each row and column sum is equal to the non-negative integer r, and such that partial line sums extending from either end along each row and column are non-negative).