Bill Doran

Counting Alternating Sign Matrices and TSSCPPs: A Survey

In the early 1980s, David Robbins along with Howard Rumsey and Bill Mills conjectured that the number of n × n alternating sign matrices is An = ∏j=0n-1 (3j+1)!⁄(n+j)!. Around the same time, they also examined a symmetry class of plane partitions: totally symmetric self-complementary plane partitions or TSSCPPs. Interestingly, they found that the number of TSSCPPs which fit inside a 2n × 2n × 2n box also equals An, at least experimentally. In the 1990s, through the efforts of many people, both of these conjectures were proven. In this talk, I will give a brief (and probably biased) survey of the paths taken to prove these conjectures. I will not assume that the audience has any familiarity with either of these conjectures or the terms involved.