共查询到13条相似文献,搜索用时 15 毫秒
1.
We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to study whether a flat rectangular algebra is a complete intersection. Along this direction, special types of algebras generated by few monomials are worked out in detail. 相似文献
2.
Let a
1,…,a
n
be relatively prime positive integers, and let S be the semigroup consisting of all non-negative integer linear combinations of a
1,…,a
n
. In this paper, we focus our attention on AA-semigroups, that is semigroups being generated by almost arithmetic progressions.
After some general considerations, we give a characterization of the symmetric AA-semigroups. We also present an efficient
method to determine an Apéry set and the Hilbert series of an AA-semigroup.
Dedicated to the memory of Ernst S. Selmer (1920–2006), whose calculations revealed the “Selmer group”. 相似文献
3.
J. C. Rosales P. A. Garcí a-Sá nchez 《Proceedings of the American Mathematical Society》2008,136(2):475-477
Let be a numerical semigroup. Then there exists a symmetric numerical semigroup such that .
4.
Víctor Blanco 《European Journal of Operational Research》2011,215(3):539-550
In this paper we present a mathematical programming formulation for the ω-invariant of a numerical semigroup for each of its minimal generators which is an useful index in commutative algebra (in particular in factorization theory) to analyze the primality of the elements in the semigroup. The model consists of solving a problem of optimizing a linear function over the efficient set of a multiobjective linear integer program. We offer a methodology to solve this problem and we provide some computational experiments to show the efficiency of the proposed algorithm. 相似文献
5.
Let g
e
(S) (respectively, g
o
(S)) be the number of even (respectively, odd) gaps of a numerical semigroup S. In this work we study and characterize the numerical semigroups S that verify 2|g
e
(S)−g
o
(S)|+1∈S. As a consequence we will see that every numerical semigroup can be represented by means of a numerical semigroup with maximal
embedding dimension with all its minimal generators odd.
The first author is supported by the project MTM2007-62346 and FEDER funds. The authors want to thank P.A. García-Sánchez
and the referee for their comments and suggestions. 相似文献
6.
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
7.
8.
We provide a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of the simplicial affine semigroups. In this way, we characterize the Cohen-Macaulay type of the simplicial affine semigroup ring . We define the type of S, , in terms of some Apéry sets of S and show that it coincides with the Cohen-Macaulay type of the semigroup ring, when is Cohen-Macaulay. If is a d-dimensional Cohen-Macaulay ring of embedding dimension at most , then . Otherwise, might be arbitrary large and it has no upper bound in terms of the embedding dimension. Finally, we present a generating set for the conductor of S as an ideal of its normalization. 相似文献
9.
In a pair of recent papers, Andrews, Fraenkel and Sellers provide a complete characterization for the number of -ary partitions modulo , with and without gaps. In this paper we extend these results to the case of coloured -ary partitions, with and without gaps. Our method of proof is different, giving explicit expansions for the generating functions modulo . 相似文献
10.
We analyze the behavior of common indices used in numerical linear algebra, analysis, and optimization to measure rates of convergence of an algorithm. A simple consistent axiomatic structure is used to uniquely define convergence rate measures on the basic linear, superlinear, and sublinear scales in terms of standard comparison sequences. Agreement with previously utilized indices and related measures is discussed.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada.The authors are grateful to the referees for comments which improved an earlier draft. 相似文献
11.
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 investigated. Let be the number of numerical semigroups of genus whose number of even gaps equals . We show that for and for ; thus the question above is true provided that for . We also show that coincides with , the number introduced by Bras-Amorós (2012) in connection with semigroup-closed sets. Finally, the stronger possibility arises being the golden number. 相似文献
12.
Cheon Seoung Ryoo 《Applied mathematics and computation》2010,216(11):3365-3369
In [8], we proposed some numerical verification methods for automatic proof of the existence of solution for obstacle problems. In this paper we propose a new iterative algorithm to automatically prove the existence of solutions for some generalized obstacle problems. 相似文献
13.
P. L. Combettes 《Applied Mathematics and Optimization》1997,35(3):311-330
The classical problem of finding a point in the intersection of countably many closed and convex sets in a Hilbert space is
considered. Extrapolated iterations of convex combinations of approximate projections onto subfamilies of sets are investigated
to solve this problem. General hypotheses are made on the regularity of the sets and various strategies are considered to
control the order in which the sets are selected. Weak and strong convergence results are established within thisbroad framework,
which provides a unified view of projection methods for solving hilbertian convex feasibility problems.
This work was supported by the National Science Foundation under Grant MIP-9308609. 相似文献