We introduce a new algebraic construction, 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.
@article{10_37236_7686,
author = {Miguel A. M\'endez and Rafael S\'anchez Lamoneda},
title = {Monops, monoids and operads: the combinatorics of {Sheffer} polynomials},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/7686},
zbl = {1393.05063},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7686/}
}
TY - JOUR
AU - Miguel A. Méndez
AU - Rafael Sánchez Lamoneda
TI - Monops, monoids and operads: the combinatorics of Sheffer polynomials
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/7686/
DO - 10.37236/7686
ID - 10_37236_7686
ER -
%0 Journal Article
%A Miguel A. Méndez
%A Rafael Sánchez Lamoneda
%T Monops, monoids and operads: the combinatorics of Sheffer polynomials
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7686/
%R 10.37236/7686
%F 10_37236_7686
Miguel A. Méndez; Rafael Sánchez Lamoneda. Monops, monoids and operads: the combinatorics of Sheffer polynomials. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7686
