J. Devillet

activity

20182020

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Showing 2018Show all

6 papers · 1 filter

math.RA2018

Classifications of quasitrivial semigroups

Jimmy Devillet, Jean-Luc Marichal, Bruno Teheux

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is…

math.CA2018

Invariance in a class of operations related to weighted quasi-geometric means

Jimmy Devillet, Janusz Matkowski

Let $I \subset (0, \infty)$ be an interval that is closed with respect to the multiplication. The operations $C_{f, g} : I^{2} \to I$ of the form \begin{equation*} C_{f,g}…

math.CA2018

A new invariance identity and means

Jimmy Devillet, Janusz Matkowski

The invariance identity involving three operations $D_{f, g} : X \times X \to X$ of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\lef…

math.RA2018

Characterizations of biselective operations

Jimmy Devillet, Gergely Kiss

Let $X$ be a nonempty set and let $i, j \in {1, 2, 3, 4}$ . We say that a binary operation $F : X^{2} \to X$ is $(i, j)$ -selective if $F (F (x_{1}, x_{2}), F (x_{3}, x_{4})) = F (x_{i}, x_{j}),$ for all $x…

math.RA2018

Associative, idempotent, symmetric, and order-preserving operations on chains

Jimmy Devillet, Bruno Teheux

We characterize the associative, idempotent, symmetric, and order-preserving operations on (finite) chains in terms of properties of (the Hasse diagram of) their associated semilat…

math.RA2018

Bisymmetric and quasitrivial operations: characterizations and enumerations

Jimmy Devillet

We investigate the class of bisymmetric and quasitrivial binary operations on a given set $X$ and provide various characterizations of this class as well as the subclass of bisymme…