3 papers
math.AC2026
Polynomials over idempotent semifields
Paul Poncet
We study univariate polynomials with coefficients in an idempotent semifield and their factorization. We do not assume the idempotent semifield under consideration to be totally or…
math.CO2025
Order-generation in posets and convolution of closure operators
Paul Poncet
Motivated by the Hofmann--Lawson theorem, which states that every continuous lattice is inf-generated by its irreducible elements, we explore how to represent posets by extreme poi…
math.GR2024
Partial metrics and normed inverse semigroups
Paul Poncet
Relying on the notions of submodular function and partial metric, we introduce normed inverse semigroups as a generalization of normed groups and sup-semilattices equipped with an…