Discrete Math Seminar <-- Click

Speaker : Masao Ishikawa (Tottori University, Japan)
Place : Class room : E6 #1409
Time : 3:00 PM ~ 4:00 PM

Title : Refined Enumeration Problems of Totally Symmetric
Self-Complementary Plane Partitions

abstract:

In this talk we give Pfaffian or determinant expressions and constant
term identities
for the conjectures in the paper
``Self-complementary totally symmetric plane partitions''
(J. Combin. Theory Ser. A 42, (1986), 277 - 292)
by W.H.~Mills, D.P.~Robbins and H.~Rumsey.
These conjectures are about weighted enumerations of certain plane partitions
and have been open more than 20 years.
We also settle a weak version of Conjecture~6 in the paper,
i.e., the number of shifted plane partitions invariant
under a certain involution is equal to the number of alternating sign matrices
invariant under the vertical flip.