2 research outputs found
On the -Enumeration of Barely Set-Valued Tableaux and Plane Partitions
Barely set-valued tableaux are a variant of Young tableaux in which one box
contains two numbers as its entry. It has recently been discovered that there
are product formulas enumerating certain classes of barely set-valued tableaux.
We give some q-analogs of these product formulas by introducing a version of
major index for these tableaux. We also give product formulas and q-analogs for
barely set-valued plane partitions. The proofs use several probability
distributions on the set of order ideals of a poset, depending on the real
parameter q > 0, which we think could be of independent interest.Comment: 38 pages, 6 tables, 3 figure