1 research outputs found
Overview of the Heisenberg--Weyl Algebra and Subsets of Riordan Subgroups
In a first part, we are concerned with the relationships between polynomials
in the two generators of the algebra of Heisenberg--Weyl, its Bargmann--Fock
representation with differential operators and the associated one-parameter
group.Upon this basis, the paper is then devoted to the groups of Riordan
matrices associated to the related transformations of matrices (i.e.
substitutions with prefunctions). Thereby, various properties are studied
arising in Riordan arrays, in the Riordan group and, more specifically, in the
`striped' Riordan subgroups; further, a striped quasigroup and a semigroup are
also examined. A few applications to combinatorial structures are also briefly
addressed in the Appendix.Comment: Version 3 of the paper entitled `On subsets of Riordan subgroups and
Heisenberg--Weyl algebra' in [hal-00974929v2]The present article is published
in The Electronic Journal of Combinatorics, Volume 22, Issue 4, 40 pages
(Oct. 2015), pp.Id: 1