Document Type
Article
Publication Date
9-27-2019
Department
Department of Mathematical Sciences
Abstract
Closed forms for fλ,i(q):=∑τ∈SYT(λ):des(τ)=iqmaj(τ)fλ,i(q):=∑τ∈SYT(λ):des(τ)=iqmaj(τ), the distribution of the major index over standard Young tableaux of given shapes and specified number of descents, are established for a large collection of λλ and ii. Of particular interest is the family that gives a positive answer to a question of Sagan and collaborators. All formulas established in the paper are unimodal, most by a result of Kirillov and Reshetikhin. Many can be identified as specializations of Schur functions via the Jacobi-Trudi identities. If the number of arguments is sufficiently large, it is shown that any finite principal specialization of any Schur function sλ(1,q,q2,…,qn−1)sλ(1,q,q2,…,qn−1) has a combinatorial realization as the distribution of the major index over a given set of tableaux.
Publication Title
The Electronic Journal of Combinatorics
Recommended Citation
Keith, W.
(2019).
Families of major index distributions: Closed forms and unimodality.
The Electronic Journal of Combinatorics,
26(3).
http://doi.org/10.37236/8585
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1225
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