Free quadri-algebras and dual quadri-algebras

Gröbner-Shirshov bases for the non-symmetric operads of dendriform algebras and quadri-algebras

On Heyting algebras and dual BCK-algebras

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

Quadri-tilings of the plane

We introduce quadri-tilings and show that they are in bijection with dimer models on a family of graphs R * arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called triangular quadri-tilings, as an interface model in dimension 2+2. Assigning “critical” weights to edges of R *, we prove an explicit expression, only depending on the local g...

on heyting algebras and dual bck-algebras

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

Ennea-algebras 1

A generalisation of a recent work of M. Aguiar and J.-L. Loday on quadri-algebras called tennea-algebras constructed over dendriform trialgebras is proposed. Such algebras allow the construction of nested dendriform trialgebras and are related to pre-Lie algebras, t-infinitesimal bialgebras and tBaxter operators. We also show that the augmented free t-ennea-algebra has a structure of connected ...