Monops, monoids and operads: the combinatorics of Sheffer polynomials
type: Item
instance of: scholarly article
title: Monops, monoids and operads: the combinatorics of Sheffer polynomials
zbMATH Open document ID: 1393.05063
author: Miguel A. Méndez
author: Rafael Sánchez Lamoneda
published in: The Electronic Journal of Combinatorics
publication date: 2018-08-15T00:00:00Z
full work available at URL: v25i3p25
review text: Summary: We introduce a new algebraic construction, \textit{monop}, that combines monoids (with respect to the product of species), and operads (monoids with respect to the substitution of species) in the same algebraic structure. By the use of properties of cancellative set-monops we construct a family of partially ordered sets whose prototypical examples are the Dowling lattices. They generalize the enriched partition posets associated to a cancellative operad, and the subset posets associated to a cancellative monoid. Their Whitney numbers of the first and second kind are the connecting coefficients of two umbral inverse Sheffer sequences with the family of powers \(\{x^n\}_{n=0}^{\infty}\). Equivalently, the entries of a Riordan matrix and its inverse. This aticle is the first part of a program in progress to develop a theory of Koszul duality for monops.
Mathematics Subject Classification ID: 05A40
Mathematics Subject Classification ID: 05E99
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 06A11
Mathematics Subject Classification ID: 18D50
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 18D10
zbMATH DE Number: 6918058
zbMATH Keywords: operads
zbMATH Keywords: monoids
zbMATH Keywords: Sheffer families
zbMATH Keywords: partition posets
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6918058