6 papers
Decomposable shuffles
João Dias, Bruno Dinis, Carlos Correia Ramos
We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural…
Bridging Meadows and Sheaves
João Dias, Bruno Dinis, Pedro Macias Marques
We bridge sheaves of rings over a topological space with common meadows (algebraic structures where the inverse for multiplication is a total operation). More specifically, we show…
Flasque Meadows
João Dias, Bruno Dinis
In analogy with flasque sheaves, we introduce the notion of flasque meadow as a common meadow where the transition maps are all surjective. We study some properties of flasque mead…
Artinian Meadows
João Dias, Bruno Dinis
We introduce the notion of Artinian meadow as an algebraic structure constructed from an Artinian ring which is also a common meadow, i.e.\ a commutative and associative structure…
Towards an Enumeration of Finite Common Meadows
João Dias, Bruno Dinis
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inve…
Strolling through common meadows
João Dias, Bruno Dinis
Meadows are a sort of commutative rings with a multiplicative identity element and a total multiplicative inverse operation. In this paper we study algebraic properties of common m…