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
On isolated gaps of numerical semigroups of embedding dimension two
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DOI: 10.1080/00927872.2024.2439500
Abstract: Abstract We explicitly describe all isolated gaps of any numerical semigroup of embedding dimension two, and we give an exact formula for the number of isolated gaps of these numerical semigroups. read more here.
Keywords: dimension two; isolated gaps; gaps numerical; numerical semigroups ... See more keywords
Construction of an endgame rulebook for Sylver Coinage using trees of numerical semigroups
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DOI: 10.1080/00927872.2025.2456089
Abstract: Abstract In this paper we show how the algorithms to explore the tree of numerical semigroups can be used to calculate the winningness of positions in the game of Sylver Coinage. We introduce a new… read more here.
Keywords: endgame rulebook; construction endgame; sylver coinage; numerical semigroups ... See more keywords
The poset of normalized ideals of numerical semigroups with multiplicity three
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DOI: 10.1080/00927872.2025.2464956
Abstract: Abstract We study the poset of normalized ideals of a numerical semigroup with multiplicity three. We show that this poset is always a lattice, and that two different numerical semigroups with multiplicity three have non-isomorphic… read more here.
Keywords: multiplicity three; normalized ideals; numerical semigroups; ideals numerical ... See more keywords
Symmetric generalized numerical semigroups in Nd with embedding dimension 2d + 1
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DOI: 10.1080/00927872.2025.2513490
Abstract: Abstract In this article, we classify all symmetric generalized numerical semigroups in Nd of embedding dimension 2d+1. Consequently, we show that in the case d>1, the property of being symmetric is equivalent to have a… read more here.
Keywords: semigroups embedding; generalized numerical; symmetric generalized; numerical semigroups ... 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
Digital numerical semigroups
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DOI: 10.2298/fil2431097m
Abstract: The number of digits in base ten system of a positive integer n, is denoted by l(n). A digital semigroup is a subsemigroup D of (N\{0}, ?) such that if d ? D, then {x… read more here.
Keywords: system; semigroup; numerical semigroup; digital numerical ... See more keywords
p-Numerical Semigroups of Triples from the Three-Term Recurrence Relations
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DOI: 10.3390/axioms13090608
Abstract: Many people, including Horadam, have studied the numbers Wn, satisfying the recurrence relation Wn=uWn−1+vWn−2 (n≥2) with W0=0 and W1=1. In this paper, we study the p-numerical semigroups of the triple (Wi,Wi+2,Wi+k) for integers i,k(≥3). For… read more here.
Keywords: term recurrence; triples three; semigroups triples; numerical semigroups ... See more keywords