Colloquium
Speaker: Alejandro Morales (UCLA)
"Hook formulas for Standard Young tableaux of skew shape"
Time: 14:30 - 15:30
Room: MC 107
Counting linear extensions of a partial order (linear orders compatible
with the partial order) is a classical and computationally difficult
problem in enumeration and computer science. A family of partial orders
that are prevalent in enumerative and algebraic combinatorics come from
Young diagrams of partitions and skew partitions. Their linear extensions
are called standard Young tableaux. The celebrated hook-length formula of
Frame, Robinson and Thrall from 1954 gives a product formula for the number
of standard Young tableaux of partition shape. No such product formula
exists for skew partitions.
In 2014, Naruse announced a formula for skew shapes as a positive sum of
products of hook-lengths using â€excited diagrams†of Ikeda-Naruse,
Kreiman, Knutson-Miller-Yong in the context of equivariant cohomology. We
prove Naruse’s formula algebraically and combinatorially in several
different ways. Also, we show how excited diagrams give asymptotic results
and product formulas for the enumeration of certain families of skew
tableaux. Lastly, we give analogues of Naruse's formula in the context of
equivariant K-theory.
This is joint work with Igor Pak and Greta Panova.