共查询到20条相似文献,搜索用时 11 毫秒
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The set of solutions of the inequality is a numerical semigroup. We present in this paper a tool for finding the set of minimal generators of this set, and thus the set of solutions to such an inequality. This tool will also enable us to give characterizations of those numerical semigroups that are the set of integer solutions of inequalities of this form. Finally, we give a deeper study of the embedding dimension three case. 相似文献
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In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup S and a semigroup ideal E?S, produces a new numerical semigroup, denoted by S? b E (where b is any odd integer belonging to S), such that S=(S? b E)/2. In particular, we characterize the ideals E such that S? b E is almost symmetric and we determine its type. 相似文献
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Charles R. Johnson 《Linear algebra and its applications》2008,429(4):875-886
There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest. 相似文献
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Aureliano M. Robles-Pérez José Carlos Rosales 《Journal of Pure and Applied Algebra》2009,213(3):387-396
Let S be a numerical semigroup and let p be a positive integer. Then the quotient is also a numerical semigroup. When p=2 we say that is half of the numerical semigroup S. Dually, we say that S is a double of the numerical semigroup . We characterize the set of all doubles of a numerical semigroup. We also give some alternative proofs and improvements for some results that we find in previous papers. 相似文献
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J. C. Rosales P. A. García-Sánchez J. I. García-García J. A. Jiménez Madrid 《Semigroup Forum》2003,67(1):145-158
We study the set of numerical semigroups containing a given numerical semigroup. As an application we prove characterizations of irreducible numerical semigroups that unify some of the existing characterizations for symmetric and pseudo-symmetric numerical semigroups. Finally we describe an algorithm for computing a minimal decomposition of a numerical semigroup in terms of irreducible numerical semigroups. 相似文献
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In this paper, we study the gender, Frobenius number and pseudo-Frobenius number for numerical semigroups with multiplicity
four, embedding dimension three and minimal generators pairwise relatively prime. 相似文献
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AbstractIn this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of arithmetic extension of a given numerical semigroup. As by-product, new explicit formulas for the Frobenius number and the genus of proportionally modular semigroups are obtained. 相似文献
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Given a numerical semigroup S=〈a 0,a 1,a 2,…,a t 〉 and n∈S, we consider the factorization n=c 0 a 0+c 1 a 1+?+c t a t where c i ≥0. Such a factorization is maximal if ∑c i is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies. 相似文献
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Let I be an interval of positive rational numbers. Then the set S (I) = T ∩ N, where T is the submonoid of (Q0+, +) generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S (I) has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals. 相似文献
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Denote by M(n) the smallest positive integer such that for every n-element monoid M there is a graph G with at most M(n) vertices such that End(G) is isomorphic to M. It is proved that . Moreover, for almost all n-element monoids M there is a graph G with at most 12 · n · log2n + n vertices such that End(G) is isomorphic to M. 相似文献
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Edward R. Scheinerman 《Journal of Graph Theory》1987,11(3):441-446
The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investigate the maximum value of the interval number for graphs with higher genus and show that the maximum value of the interval number of graphs with genus g is between ?√g? and 3 + ?√3g?. We also show that the maximum arboricity of graphs with genus g is either 1 + ?√3g? or 2 + ?√3g?. 相似文献
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Víctor Blanco 《Semigroup Forum》2013,87(2):407-427
In this paper we analyze the irreducibility of numerical semigroups with multiplicity up to four. Our approach uses the notion of Kunz-coordinates vector of a numerical semigroup recently introduced in Blanco and Puerto (SIAM J. Discrete Math., 26(3):1210–1237, 2012). With this tool we also completely describe the whole family of minimal decompositions into irreducible numerical semigroups with the same multiplicity for this set of numerical semigroups. We give detailed examples to show the applicability of the methodology and conditions for the irreducibility of well-known families of numerical semigroups such as those that are generated by a generalized arithmetic progression. 相似文献
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We characterize the extremal digraphs which attain the maximum Perron root of digraphs with given arc connectivity and number of vertices. We also characterize the extremal digraphs which attain the maximum Perron root of digraphs given diameter and number of vertices. 相似文献
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J. C. Rosales 《Proceedings of the American Mathematical Society》2001,129(8):2197-2203
We construct symmetric numerical semigroups for every minimal number of generators and multiplicity , . Furthermore we show that the set of their defining congruence is minimally generated by elements.
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Computational Management Science - This paper introduces a fractional version of the classical maximum weight clique problem, the maximum ratio clique problem, which is to find a maximal clique... 相似文献
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Guo-Hui Zhang 《Journal of Graph Theory》1992,16(3):205-211
The odd girth of a graph G is the length of a shortest odd cycle in G. Let d(n, g) denote the largest k such that there exists a k-regular graph of order n and odd girth g. It is shown that dn, g ≥ 2|n/g≥ if n ≥ 2g. As a consequence, we prove a conjecture of Pullman and Wormald, which says that there exists a 2j-regular graph of order n and odd girth g if and only if n ≥ gj, where g ≥ 5 is odd and j ≥ 2. A different variation of the problem is also discussed. 相似文献