A new generalization of binomial coefficients

Abstract

Let t be a fixed parameter and x some indeterminate. We give some properties of the generalized binomial coefficients x k inductively defined by k/

Class expansion of some symmetric functions in Jucys–Murphy elements

“…But a general formula for ψ ρ (t) is lacking even when ρ is a hook (r, 1 s ). The case of hooks is only known for 0 ≤ s ≤ 3, in which cases the structure of ψ (r,1 s ) (t) is already very messy [22].…”