共查询到20条相似文献,搜索用时 36 毫秒
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Ping Sun 《Discrete Mathematics》2012,312(24):3649-3655
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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
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Liuquan Wang 《Discrete Mathematics》2018,341(12):3370-3384
Let be the number of -colored generalized Frobenius partitions of . We establish some infinite families of congruences for and modulo arbitrary powers of 3, which refine the results of Kolitsch. For example, for and , we prove that We give two different proofs to the congruences satisfied by . One of the proofs uses a relation between and due to Kolitsch, for which we provide a new proof in this paper. 相似文献
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Ping Sun 《Discrete Mathematics》2018,341(4):1144-1149
This paper considers the enumeration problem of a generalization of standard Young tableau (SYT) of truncated shape. Let be the SYT of shape truncated by whose upper left cell is , where and are partitions of integers. The summation representation of the number of SYT of the truncated shape is derived. Consequently, three closed formulas for SYT of hollow shapes are obtained, including the cases of (i). , (ii). , and (iii). . Finally, an open problem is posed. 相似文献
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《Discrete Mathematics》2007,307(17-18):2217-2225
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Hossein Hajiabolhassan 《Discrete Mathematics》2011,311(23-24):2663-2668
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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
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Susan A. van Aardt Christoph Brause Alewyn P. Burger Marietjie Frick Arnfried Kemnitz Ingo Schiermeyer 《Discrete Mathematics》2017,340(11):2673-2677
An edge-coloured graph is called properly connected if any two vertices are connected by a path whose edges are properly coloured. The proper connection number of a connected graph denoted by , is the smallest number of colours that are needed in order to make properly connected. Our main result is the following: Let be a connected graph of order and . If , then except when and where and 相似文献
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《Discrete Mathematics》2007,307(17-18):2209-2216
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