Dilatations of numerical semigroups
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DOI: 10.1007/s00233-018-9922-9
Abstract: This paper is focused on numerical semigroups and presents a simple construction, that we call “dilatation”, which, from a starting semigroup S, permits to get an infinite family of semigroups which share several properties with… read more here.
Keywords: dilatations numerical; semigroup; numerical semigroups;
Irreducible generalized numerical semigroups and uniqueness of the Frobenius element
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DOI: 10.1007/s00233-019-10040-1
Abstract: Let $$\mathbb {N}^{d}$$Nd be the d-dimensional monoid of non-negative integers. A generalized numerical semigroup is a submonoid $$ S\subseteq \mathbb {N}^d$$S⊆Nd such that $$H(S)=\mathbb {N}^d \backslash S$$H(S)=Nd\S is a finite set. We introduce irreducible generalized… read more here.
Keywords: frobenius element; semigroups uniqueness; numerical semigroups; irreducible generalized ... See more keywords
Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups
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DOI: 10.1080/00927872.2022.2034837
Abstract: For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factorizations of semigroup elements. This work generalizes many previous results, provides… read more here.
Keywords: weighted factorization; factorization lengths; numerical semigroups; factorization length ... See more keywords
Numerical semigroups and periodic orbits for Markov interval maps
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DOI: 10.1080/10236198.2017.1351558
Abstract: Abstract Interval maps constitute a very important class of discrete dynamical systems with a well developed theory. Our purpose in this paper is to study a particular class of interval maps for which the set… read more here.
Keywords: markov interval; numerical semigroups; orbits markov; interval maps ... See more keywords
Algorithms for generalized numerical semigroups
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DOI: 10.1142/s0219498821500791
Abstract: We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of [Formula: see text] with finite complement in [Formula: see text]. These semigroups are affine semigroups, which in particular implies that they… read more here.
Keywords: see text; numerical semigroups; generalized numerical; formula see ... See more keywords
Numerical semigroups bounded by a cyclic monoid
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DOI: 10.7153/jmi-2021-15-81
Abstract: We will say that a numerical semigroup S is bounded by a cyclic monoid if there exist integer numbers 0 α < β such that S = {x ∈ N | kα < x <… read more here.
Keywords: cyclic monoid; semigroups bounded; bounded cyclic; numerical semigroups ... See more keywords