Abstract
The purpose of this paper is to present the $q$-hook formula of Gansner type for a generalized Young diagram in the sense of D. Peterson and R. A. Proctor. This gives a far-reaching generalization of a hook length formula due to J. S. Frame, G. de B. Robinson, and R. M. Thrall. Furthurmore, we give a generalization of P. MacMahon's identity as an application of the $q$-hook formula. Le but de ce papier est présenter la $q$-hook formule de type Gansner pour un Young diagramme généralisé dans le sens de D. Peterson et R. A. Proctor. Cela donne une généralisation de grande envergure d'une hook length formule dû à J. S. Frame, G. de B. Robinson, et R. M. Thrall. Furthurmore, nous donnons une généralisation de l'identité de P. MacMahon comme une application de la $q$-hook formule.
Highlights
IntroductionLet P = (P ; ≤) be a finite partially ordered set
The purpose of this paper is to present a generalization of (1.1) for a generalized Young diagram in the sense of D
These give the identities for the generating function of shifted plane partitions
Summary
Let P = (P ; ≤) be a finite partially ordered set. The set of linear extensions of (P ; ≤) is denoted by L (P ; ≤) Remark 2.4 In section 7, we consider a certain infinite partially ordered set with a certain infinte colorset I In such a situation, we define a notion of (P ; ≤)-partitions as follows: We define a lattice Q by: Q = Zαi, i∈I where αi i ∈ I is a formal basis. A (possibly infinite) partially ordered set (P ; ≤) is said to be a (c; I)-compatible poset if: For each φ ∈ Q, there exists at most finitely many σ ∈ A (P ; ≤) such that v∈P σ(v)αc(v) = φ
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
