6 papers
On atoms of the set of generalized numerical semigroups with fixed corner element
Matheus Bernardini, Alonso S. Castellanos, Wanderson Tenório +1
We study the so-called atomic GNS, which naturally extends the concept of atomic numerical semigroup. We introduce the notion of corner special gap and we characterize the class of…
Gapsets and the -generalized Fibonacci sequences
Gilberto B. Almeida Filho, Matheus Bernardini
In this paper, we bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to -extensions. It allows us to identify gapset…
A generalization of a theorem about gapsets with depth at most three
Matheus Bernardini, Patrick Melo
In this paper, we provide a generalization of a theorem proved by Eliahou and Fromentin, which exhibit a remarkable property of the sequence , where denotes the numb…
The corner element of generalized numerical semigroups
Matheus Bernardini, Wanderson Tenório, Guilherme Tizziotti
In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalize…
Counting numerical semigroups by genus and even gaps via Kunz-coordinate vectors
Matheus Bernardini
We contruct a one-to-one correspondence between a subset of numerical semigroups with genus and even gaps and the integer points of a rational polytope. In particular, we g…
Counting numerical semigroups by genus and even gaps
Matheus Bernardini, Fernando Torres
Let be the number of numerical semigroups of genus . We present an approach to compute by using even gaps, and the question: Is it true that ? is invest…