Path decompositions of digraphs and their applications to Weyl algebra
Combinatorics
2015-03-26 v2 Rings and Algebras
Abstract
We consider decompositions of digraphs into edge-disjoint paths and describe their connection with the -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 -Stirling functions which enumerate decompositions by sources (and sinks) of paths.
Keywords
Cite
@article{arxiv.1408.6764,
title = {Path decompositions of digraphs and their applications to Weyl algebra},
author = {Askar Dzhumadil'daev and Damir Yeliussizov},
journal= {arXiv preprint arXiv:1408.6764},
year = {2015}
}