共查询到20条相似文献,搜索用时 15 毫秒
1.
Maria Bras-Amorós 《Journal of Pure and Applied Algebra》2009,213(6):997-1001
Lower and upper bounds are given for the number ng of numerical semigroups of genus g. The lower bound is the first known lower bound while the upper bound significantly improves the only known bound given by the Catalan numbers. In a previous work the sequence ng is conjectured to behave asymptotically as the Fibonacci numbers. The lower bound proved in this work is related to the Fibonacci numbers and so the result seems to be in the direction to prove the conjecture. The method used is based on an accurate analysis of the tree of numerical semigroups and of the number of descendants of the descendants of each node depending on the number of descendants of the node itself. 相似文献
2.
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
3.
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
4.
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
5.
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
6.
7.
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
8.
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
9.
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
10.
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
11.
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
12.
13.
Micha Sharir 《Combinatorica》1988,8(1):117-124
We derive lower bounds on the maximal length
s(n) of (n, s) Davenport Schinzel sequences. These bounds have the form 2s=1(n)=(ns(n)), where(n) is the extremely slowly growing functional inverse of the Ackermann function. These bounds extend the nonlinear lower bound
3
(n)=(n(n)) due to Hart and Sharir [5], and are obtained by an inductive construction based upon the construction given in [5].Work on this paper has been supported by Office of Naval Research Grant N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation, and the IBM Corporation. 相似文献
14.
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
15.
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
16.
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
17.
Jiaojiao Wu 《Discrete Mathematics》2008,308(12):2637-2642
This paper discusses the game colouring number of partial k-trees and planar graphs. Let colg(PTk) and colg(P) denote the maximum game colouring number of partial k trees and the maximum game colouring number of planar graphs, respectively. In this paper, we prove that colg(PTk)=3k+2 and colg(P)?11. We also prove that the game colouring number colg(G) of a graph is a monotone parameter, i.e., if H is a subgraph of G, then colg(H)?colg(G). 相似文献
18.
Suppose G is a graph and λ1,λ2,…,λn are the eigenvalues of G. The Estrada index EE(G) of G is defined as the sum of eλi, 1≤i≤n. In this paper some new upper bounds for the Estrada index of bipartite graphs are presented. We apply our result on a (4,6)-fullerene to improve our bound given in an earlier paper. 相似文献
19.
20.
Bettina Richmond 《Topology and its Applications》2008,155(15):1644-1649
For a given set X, the set F(X) of all maps from X to X forms a semigroup under composition. A subsemigroup S of F(X) is said to be saturated if for each x∈X there exists a set Ox⊆X with x∈Ox such that . It is shown that there exists a one-to-one correspondence between principal topologies on X and saturated subsemigroups of F(X). Some properties of principal topologies on X and the corresponding properties of their associated saturated subsemigroups of F(X) are discussed. 相似文献