共查询到20条相似文献,搜索用时 31 毫秒
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Partitioning a set into similar, if not, identical, parts is a fundamental research topic in combinatorics. The question of partitioning the integers in various ways has been considered throughout history. Given a set of integers where , let the gap sequence of this set be the unordered multiset . This paper addresses the following question, which was explicitly asked by Nakamigawa: can the set of integers be partitioned into sets with the same gap sequence? The question is known to be true for any set where the gap sequence has length at most two. This paper provides evidence that the question is true when the gap sequence has length three. Namely, we prove that given positive integers and , there is a positive integer such that for all , the set of integers can be partitioned into 4-sets with gap sequence , . 相似文献
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DP-coloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each , every planar graph without is 4-choosable. Furthermore, Jin et al. (2016) showed that for each , every signed planar graph without is signed 4-choosable. In this paper, we show that for each , every planar graph without is 4-DP-colorable, which is an extension of the above results. 相似文献
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Ercan Sönmez 《Stochastic Processes and their Applications》2018,128(2):426-444
Let be a multivariate operator-self-similar random field with values in . Such fields were introduced in [22] and satisfy the scaling property for all , where is a real matrix and is an real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of and as well as the multiplicity of the eigenvalues of and . 相似文献
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Effect of stochastic perturbations for front propagation in Kolmogorov Petrovskii Piscunov equations
John M. Noble 《Stochastic Processes and their Applications》2018,128(10):3531-3557
This article considers equations of Kolmogorov Petrovskii Piscunov type in one space dimension, with stochastic perturbation: where the stochastic differential is taken in the sense of Itô and is a Gaussian random field satisfying and . Two situations are considered: firstly, is simply a standard Wiener process (i.e. ): secondly, with .The results are as follows: in the first situation (standard Wiener process: i.e. ), there is a non-degenerate travelling wave front if and only if , with asymptotic wave speed ; the noise slows the wave speed. If the stochastic integral is taken instead in the sense of Stratonovich, then the asymptotic wave speed is the classical McKean wave speed and does not depend on .In the second situation (noise with spatial covariance which decays to 0 at , stochastic integral taken in the sense of Itô), a travelling front can be defined for all . Its average asymptotic speed does not depend on and is the classical wave speed of the unperturbed KPP equation. 相似文献
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Serhii Dyshko 《Discrete Mathematics》2018,341(11):2995-3002
For a finite vector space over , there are described all the pairs of multisets and of subspaces in such that for all the equality holds. 相似文献
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Xiuyun Wang 《Discrete Mathematics》2017,340(12):3016-3019
The double generalized Petersen graph , and , , has vertex-set , edge-set . These graphs were first defined by Zhou and Feng as examples of vertex-transitive non-Cayley graphs. Then, Kutnar and Petecki considered the structural properties, Hamiltonicity properties, vertex-coloring and edge-coloring of , and conjectured that all are Hamiltonian. In this paper, we prove this conjecture. 相似文献
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Guan-Huei Duh Yen-Chi Roger Lin Shi-Mei Ma Yeong-Nan Yeh 《Discrete Mathematics》2018,341(9):2478-2484
A permutation of the multiset is called a Stirling permutation of order if every entry between the two occurrences of is greater than for each . In this paper, we introduce the definitions of block, even indexed entry, odd indexed entry, Stirling derangement, marked permutation and bicolored increasing binary tree. We first study the joint distribution of ascent plateaux, even indexed entries and left-to-right minima over the set of Stirling permutations of order . We then present an involution on Stirling derangements. 相似文献
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Ce Xu 《Comptes Rendus Mathematique》2018,356(3):243-252
Recently, Dil and Boyadzhiev [10] proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence . In this paper, we show that the sums of multiple harmonic numbers whose indices are the sequence can be expressed in terms of (multiple) zeta values, (multiple) harmonic numbers, and Stirling numbers of the first kind, and give an explicit formula. 相似文献
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Let is an independent set of a graph G. In this paper, we give a low bound for the length of a longest cycle in a 4-connected graph and get the following result: If is a 4-connected graph on vertices, then the circumference . Moreover, we give graphs to show that the connectivity in our result is best possible with respect to the low bound and the low bound in our result is also best possible with respect to the connectivity. 相似文献
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The -power graph of a graph is a graph with the same vertex set as , in that two vertices are adjacent if and only if, there is a path between them in of length at most . A -tree-power graph is the -power graph of a tree, a -leaf-power graph is the subgraph of some -tree-power graph induced by the leaves of the tree.We show that (1) every -tree-power graph has NLC-width at most and clique-width at most , (2) every -leaf-power graph has NLC-width at most and clique-width at most , and (3) every -power graph of a graph of tree-width has NLC-width at most , and clique-width at most . 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