共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
In this paper, we consider combinatorial numbers , mentioned as Catalan triangle numbers where . These numbers unify the entries of the Catalan triangles and for appropriate values of parameters and , i.e., and . In fact, these numbers are suitable rearrangements of the known ballot numbers and some of these numbers are the well-known Catalan numbers that is .We present identities for sums (and alternating sums) of , squares and cubes of and, consequently, for and . In particular, one of these identities solves an open problem posed in Gutiérrez et al. (2008). We also give some identities between and harmonic numbers . Finally, in the last section, new open problems and identities involving are conjectured. 相似文献
3.
TextFor any given two positive integers and , and any set A of nonnegative integers, let denote the number of solutions of the equation with . In this paper, we determine all pairs of positive integers for which there exists a set such that for all . We also pose several problems for further research.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EnezEsJl0OY. 相似文献
4.
5.
Ping Sun 《Discrete Mathematics》2012,312(24):3649-3655
6.
7.
8.
Bart Litjens 《Discrete Mathematics》2018,341(6):1740-1748
9.
11.
Let and denote the maximum degree and the Laplacian spectral radius of a tree , respectively. In this paper we prove that for two trees and on vertices, if and , then , and the bound “” is the best possible. We also prove that for two trees and on vertices with perfect matchings, if and , then . 相似文献
12.
13.
14.
Yong-Gao Chen 《Comptes Rendus Mathematique》2018,356(2):121-124
Recently, motivated by Stanley's sequences, Kiss, Sándor, and Yang introduced a new type sequence: a sequence A of nonnegative integers is called an -covering sequence if there exists an integer such that, if , then there exist , such that form a k-term arithmetic progression. They prove that there exists an -covering sequence A such that . In this note, we prove that there exists an -covering sequence A such that . 相似文献
15.
16.
Ryan Alweiss 《Discrete Mathematics》2018,341(4):981-989
The generalized Ramsey number is the smallest positive integer such that any red–blue coloring of the edges of the complete graph either contains a red copy of or a blue copy of . Let denote a cycle of length and denote a wheel with vertices. In 2014, Zhang, Zhang and Chen determined many of the Ramsey numbers of odd cycles versus larger wheels, leaving open the particular case where is even and . They conjectured that for these values of and , . In 2015, Sanhueza-Matamala confirmed this conjecture asymptotically, showing that . In this paper, we prove the conjecture of Zhang, Zhang and Chen for almost all of the remaining cases. In particular, we prove that if , , and . 相似文献
17.
A graph is packable if it is a subgraph of its complement. The following statement was conjectured by Faudree, Rousseau, Schelp and Schuster in 1981: every non-star graph with girth at least is packable.The conjecture was proved by Faudree et al. with the additional condition that has at most edges. In this paper, for each integer , we prove that every non-star graph with girth at least and at most edges is packable, where is for every . This implies that the conjecture is true for sufficiently large planar graphs. 相似文献
18.
19.
An configuration is a set of points and lines such that each point lies on lines while each line contains points. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. The existence and enumeration of configurations for a given has been subject to active research. A current front of research concerns geometric configurations: it is now known that geometric configurations exist for all , apart from sporadic exceptional cases. In this paper, we settle by computational techniques the first open case of configurations: we obtain all topological configurations among which none are geometrically realizable. 相似文献
20.
Let denote the largest possible size among all -OOCs. An -OOC with codewords is said to be optimal. In this paper, the exact value of is determined. Equivalently, the size of an optimal optical orthogonal code is calculated. 相似文献