Polynomiality of Certain Average Weights for Oscillating Tableaux

Abstract

We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived.

Area Statistics for Large Oscillating Tableaux

“…Figure 5 compare the above equations to the numerically sampled volume when N is large. Note that in [5] (Theorem 1.3), the authors extended the above by showing the polynomality of certain weighted averages of oscillating tableaux. It is easy to rephrase there results in this setting.…”

“…It is a well-known fact that the number of such tableaux for fixed shape and length has a very simple formula. λ (0) = ∅, λ (1) = , λ (2) = , λ (3) = , λ (4) = , λ (5) = Figure 1. An example of an oscillating tableaux of shape λ = (2, 1) and length N = 5.…”