排序方式: 共有110条查询结果,搜索用时 15 毫秒
1.
Jang Soo Kim 《Journal of Combinatorial Theory, Series A》2011,118(4):1168-1189
We interpret noncrossing partitions of type B and type D in terms of noncrossing partitions of type A. As an application, we get type-preserving bijections between noncrossing and nonnesting partitions of type B, type C and type D which are different from those in the recent work of Fink and Giraldo. We also define Catalan tableaux of type B and type D, and find bijections between them and noncrossing partitions of type B and type D respectively. 相似文献
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Arzad A. Kherani 《Queueing Systems》2006,53(3):159-169
In this paper we present a direct approach to obtaining joint distributions of various quantities of interest in a busy period
in an M/M/1 queue. These quantities are: the sojourn times and waiting times of all the customers in the busy period, the busy period length and the number of customers served in a busy period. Since the evolution
of the total workload process between two successive customer arrivals is deterministic, this work gives statistic of the
complete evolution of the workload process within a busy period.
This work was done when the author was post doctoral fellow with the MAESTRO group at INRIA, Sophia Antipolis, France, and
was supported by project no. 2900-IT-1 from the Centre Franco-Indien pour la Promotion de la Recherche Avancee (CEFIPRA). 相似文献
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Jakob Jonsson 《Journal of Combinatorial Theory, Series A》2005,112(1):117-142
For n?3, let Ωn be the set of line segments between vertices in a convex n-gon. For j?1, a j-crossing is a set of j distinct and mutually intersecting line segments from Ωn such that all 2j endpoints are distinct. For k?1, let Δn,k be the simplicial complex of subsets of Ωn not containing any (k+1)-crossing. For example, Δn,1 has one maximal set for each triangulation of the n-gon. Dress, Koolen, and Moulton were able to prove that all maximal sets in Δn,k have the same number k(2n-2k-1) of line segments. We demonstrate that the number of such maximal sets is counted by a k×k determinant of Catalan numbers. By the work of Desainte-Catherine and Viennot, this determinant is known to count quite a few other objects including fans of non-crossing Dyck paths. We generalize our result to a larger class of simplicial complexes including some of the complexes appearing in the work of Herzog and Trung on determinantal ideals. 相似文献
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最近,孙华定义了一类新的精细化Eulerian多项式,即$$A_n(p,q)=\sum_{\pi\in \mathfrak{S}_n}p^{{\rm odes}(\pi)}q^{{\rm edes}(\pi)},\ \ n\ge 1,$$ 其中$S_n$表示$\{1,2,\ldots,n\}$上全体$n$阶排列的集合, odes$(\pi)$与edes$(\pi)$分别表示$S_n$中排列$\pi$的奇数位与偶数位上降位数的个数.本文利用经典的Eulerian多项式$A_n(q)$ 与Catalan 序列的生成函数$C(q)$,得到精细化Eulerian 多项式$A_n(p,q)$的指数型生成函数及$A_n(p,q)$的显示表达式.在一些特殊情形,本文建立了$A_n(p,q)$与$A_n(0,q)$或$A_n(p,0)$之间的联系,并利用Eulerian数表示多项式$A_n(0,q)$的系数.特别地,这些联系揭示了Euler数$E_n$与Eulerian数$A_{n,k}$之间的一种新的关系. 相似文献
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XinRongMA 《数学学报(英文版)》2004,20(1):157-162
In two centuries ago,Ming Autu discovered the famous Catalan numbers while he tried to expand the function sin(2px) as power series of sin(x) for the case p=1,2,3.Very recently,P.J.Larcombe shows that for any p,sin(2px) can always be expressed as an infinite power series of sin(x) involving precise combinations of Catalan numbers as part of all but the initial p terms and gave all expansions for the case p=4,5.The present paper presents the desired expansion for arbitrary integer p. 相似文献
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Benjamin Braun Hugo Corrales Scott Corry Luis David García Puente Darren Glass Nathan Kaplan Jeremy L. Martin Gregg Musiker Carlos E. Valencia 《Discrete Mathematics》2018,341(10):2949-2963
Let be a finite, connected graph. An arithmetical structure on is a pair of positive integer vectors such that , where is the adjacency matrix of . We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices ). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles. 相似文献
10.
Zeph A. Landau 《Geometriae Dedicata》2002,95(1):183-214
An inclusion of II
1 factors NM of finite index has as an invariant, a double sequence of finite-dimensional algebras known as the standard invariant. Planar algebras were introduced by V. Jones as a geometric tool for computing standard invariants of existing subfactors as well as generating standard invariants for new subfactors. In this paper we define a class of planar algebras, termed exchange relation planar algebras, that provides a general framework for understanding several classes of known subfactor inclusions: the Fuss–Catalan algebras (i.e. those coming from the presence of intermediate subfactors) and all depth 2 subfactors. In addition, we present a new class of planar algebras (and thus a new class of subfactors) coming from automorphism subgroups of finite groups. 相似文献