Related papers: Exploring the tree of numerical semigroups
We introduce an algorithmic approach based on generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate…
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…
For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every…
In this paper we present a mathematical formulation for the omega invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a…
We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set of any affine semigroup, (ii) an improved method of…
The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of…
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…
We present a new way of constructing an ensemble classifier, named the Guided Random Forest (GRAF) in the sequel. GRAF extends the idea of building oblique decision trees with localized partitioning to obtain a global partitioning. We show…
The use of compositions simplifies some aspects of the theory of numerical semigroups. We illustrate this by giving a new proof for the asymptotic number C((1 + $\sqrt$ 5)/2) g of numerical semigroups of genus g and by describing the…
In 2013, Zhai proved that most numerical semigroups of a given genus have depth at most $3$ and that the number $n_g$ of numerical semigroups of a genus $g$ is asymptotic to $S\varphi^g$, where $S$ is some positive constant and $\varphi…
A novel simulation strategy is proposed to search for semiconductor quantum devices which are optimized with respect to required performances. Based on evolutionary programming, a tecnique implementing the paradigm of genetic algorithms to…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
In this article, we study the quotients of numerical semigroups, generated by two coprime positive numbers, named (a,b) over d. We give formulae for the usual invariants of these semigroups, expressed in terms of continued fraction…
In 2015, Guth proved that if $S$ is a collection of $n$ $g$-dimensional semi-algebraic sets in $\mathbb{R}^d$ and if $D\geq 1$ is an integer, then there is a $d$-variate polynomial $P$ of degree at most $D$ so that each connected component…
We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have negative Eliahou number in terms of its…
Networks are ubiquitous in biology and computational approaches have been largely investigated for their inference. In particular, supervised machine learning methods can be used to complete a partially known network by integrating various…
This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tree} that serves as a valuable tool for further analysis.…
We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional…
In this paper we introduce the new concepts of supersymmetric and self-symmetric gaps of a numerical semigroup with two generators. Those concepts are based on certain symmetries of the gaps of the semigroup with respect to their Wilf…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…