2019/01/01 by L. Wyatt Alverson, Alverson, L. Wyatt, Robert G. Donnelly +5
Mathematics · #05E05 (Primary) 05A15 #05E10 #17B10 (Secondary) #20F55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1901.00185
openalex publication_date 2019/01/01 · openalex created_date 2022/07/31 · openalex updated_date 2026/07/28
In prior work, the authors, along with M. McClard, R. A. Proctor, and N. J.\nWildberger, studied certain distributive lattice models for the `Weyl\nbialternants' (aka `Weyl characters') associated with the rank two root\nsystems/Weyl groups. These distributive lattices were uniformly described as\nlattices of order ideals taken from certain grid-like posets, although the\narguments connecting the lattices to Weyl bialternants were case-by-case\ndepending on the type of the rank two root system. Using this connection with\nWeyl bialternants, these lattices were shown to be rank symmetric and rank\nunimodal, and their rank generating functions were shown to have beautiful\nquotient-of-products expressions. Here, these results are re-derived from\nscratch using completely uniform and elementary combinatorial reasoning in\nconjunction with some combinatorial methodology developed elsewhere by the\nsecond listed author.\n