**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).