共查询到20条相似文献,搜索用时 15 毫秒
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J.C. Rosales 《Linear algebra and its applications》2009,430(1):41-51
Given a positive integer g, we denote by F(g) the set of all numerical semigroups with Frobenius number g. The set (F(g),∩) is a semigroup. In this paper we study the generators of this semigroup. 相似文献
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Charles Almeida Aline V. Andrade Rosa M. Miró-Roig 《Journal of Pure and Applied Algebra》2019,223(4):1817-1831
Let be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators of lies in the interval . In this paper, we prove that for and , the integer values in cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems of forms of degree d with or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for , and there exists a minimal monomial Togliatti system of forms of degree d with . 相似文献
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Anna Oneto 《Journal of Pure and Applied Algebra》2008,212(10):2271-2283
Let S={s0=0<s1<?<si…}⊆N be a numerical non-ordinary semigroup; then set, for each . We find a non-negative integer m such that dORD(i)=νi+1 for i≥m, where dORD(i) denotes the order bound on the minimum distance of an algebraic geometry code associated to S. In several cases (including the acute ones, that have previously come up in the literature) we show that this integer m is the smallest one with the above property. Furthermore it is shown that every semigroup generated by an arithmetic sequence or generated by three elements is acute. For these semigroups, the value of m is also found. 相似文献
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Grothendieck polynomials, introduced by Lascoux and Schützenberger, are certain K-theory representatives for Schubert varieties. Symplectic Grothendieck polynomials, described more recently by Wyser and Yong, represent the K-theory classes of orbit closures for the complex symplectic group acting on the complete flag variety. We prove a transition formula for symplectic Grothendieck polynomials and study their stable limits. We show that each of the K-theoretic Schur P-functions of Ikeda and Naruse arises from a limiting procedure applied to symplectic Grothendieck polynomials representing certain “Grassmannian” orbit closures. 相似文献
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Igor Dolinka 《Journal of Pure and Applied Algebra》2009,213(10):1979-1990
We show that a finite completely regular semigroup has a sub-log-exponential free spectrum if and only if it is locally orthodox and has nilpotent subgroups. As a corollary, it follows that the Seif Conjecture holds true for completely regular monoids. In the process, we derive solutions of word problems of free objects in a sequence of varieties of locally orthodox completely regular semigroups from solutions of word problems in relatively free bands. 相似文献
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In this paper, we characterize those numerical semigroups containing 〈n1,n2〉. From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators. 相似文献
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Maria Bras-Amorós 《Semigroup Forum》2008,76(2):379-384
We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that
the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the number of
semigroups of genus at most 50. The Wilf conjecture has also been checked for all numerical semigroups with genus in the same
range. 相似文献
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Taíse Santiago Costa Oliveira 《Discrete Mathematics》2008,308(1):148-152
We prove that certain numbers occurring in a problem of paths enumeration, studied by Niederhausen in [Catalan traffic at the beach, Eletron. J. Combin. 9 (R33) (2002) 1-17] (see also [R.P. Stanley, Catalan addendum, version of 30 October 2005. 〈http://www-math.mit.edu/∼rstan/ec/catadd.pdf〉]), are top intersection numbers in the cohomology ring of the Grassmannian of the lines in the complex projective (n+1)- space. 相似文献
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Let S be a multiplicative semigroup of matrices with nonnegative entries. Assume that the diagonal entries of the members of S form a finite set. This paper is concerned with the following question: Under what circumstances can we deduce that S itself is finite? 相似文献
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Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate three by three Hermitian matrices is given, and the structure of the corresponding coordinate ring as a module over the special unitary group is determined. The method applies also for degenerate real symmetric three by three matrices. For arbitrary n partial information on the minimal degree component of the vanishing ideal of the variety of n×n Hermitian matrices with a bounded number of eigenvalues is obtained, and some known results on sum of squares presentations of subdiscriminants of real symmetric matrices are extended to the case of complex Hermitian matrices. 相似文献
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Yufei Zhao 《Semigroup Forum》2010,80(2):242-254
Let n g denote the number of numerical semigroups of genus g. Bras-Amorós conjectured that n g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree. We offer a new, simpler approach to counting numerical semigroups of a given genus. Our method gives direct constructions of families of numerical semigroups, without referring to the generators or the semigroup tree. In particular, we give an improved asymptotic lower bound for n g . 相似文献
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We study various aspects of how certain positivity assumptions on complex matrix semigroups affect their structure. Our main result is that every irreducible group of complex matrices with nonnegative diagonal entries is simultaneously similar to a group of weighted permutations. We also consider the corresponding question for semigroups and discuss the effect of the assumption that a fixed linear functional has nonnegative values when restricted to a given semigroup. 相似文献
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Thomas Stehling 《Combinatorica》1992,12(4):475-479
We consider the numberN
A
(r) of subgroups of orderp
r
ofA, whereA is a finite Abelianp-group of type =1,2,...,
l
()), i.e. the direct sum of cyclic groups of order ii. Formulas for computingN
A
(r) are well known. Here we derive a recurrence relation forN
A
(r), which enables us to prove a conjecture of P. E. Dyubyuk about congruences betweenN
A
(r) and the Gaussian binomial coefficient
. 相似文献
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Calin Chindris 《Journal of Pure and Applied Algebra》2009,213(7):1418-1429
We show that a finite, connected quiver Q without oriented cycles is a Dynkin or Euclidean quiver if and only if all orbit semigroups of representations of Q are saturated. 相似文献
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This paper studies the problem of estimating the spectral radius of trees with the given number of vertices and maximum degree. We obtain the new upper bounds on the spectral radius of the trees, and the results are the best upper bounds expressed by the number of vertices and maximum degree, at present. 相似文献