2010/05/20 by Sami Assaf, Sami H. Assaf, Assaf, Sami H. · 2 citations
Chemistry · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #math.CO
paper · pdf · doi:10.48550/arxiv.1005.3759
59 pages, 51 figures, now includes Maple code
openalex publication_date 2010/05/20 · arxiv created 2013/10/23 · arxiv updated 2013/10/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. By constructing a graph on ribbon tableaux which we transform into a dual equivalence graph, we give a combinatorial proof of the symmetry and Schur positivity of the ribbon tableaux generating functions introduced by Lascoux, Leclerc and Thibon. Using Haglund's formula for the transformed Macdonald polynomials, this also gives a combinatorial formula for the Schur expansion of Macdonald polynomials.