2014/08/28 by Askar Dzhumadil'daev, Askar Dzhumadil’daev, Damir Yeliussizov +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #math.CO #math.RA
paper · pdf · doi:10.48550/arxiv.1408.6764
openalex publication_date 2014/08/28 · arxiv created 2015/03/25 · arxiv updated 2015/03/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We consider decompositions of digraphs into edge-disjoint paths and describe their connection with the n-th Weyl algebra of differential operators. This approach gives a graph-theoretic combinatorial view of the normal ordering problem and helps to study skew-symmetric polynomials on certain subspaces of Weyl algebra. For instance, path decompositions can be used to study minimal polynomial identities on Weyl algebra, similar as Eulerian tours applicable for Amitsur--Levitzki theorem. We introduce the G-Stirling functions which enumerate decompositions by sources (and sinks) of paths.