共查询到20条相似文献,搜索用时 31 毫秒
1.
In the papers (Benoumhani 1996;1997), Benoumhani defined two polynomials and . Then, he defined and to be the polynomials satisfying and . In this paper, we give a combinatorial interpretation of the coefficients of and prove a symmetry of the coefficients, i.e., . We give a combinatorial interpretation of and prove that is a polynomial in with non-negative integer coefficients. We also prove that if then all coefficients of except the coefficient of are non-negative integers. For all , the coefficient of in is , and when some other coefficients of are also negative. 相似文献
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For given graphs , , the -color Ramsey number, denoted by , is the smallest integer such that if we arbitrarily color the edges of a complete graph of order with colors, then it always contains a monochromatic copy of colored with , for some . Let be a cycle of length and a star of order . In this paper, firstly we give a general upper bound of . In particular, for the 3-color case, we have and this bound is tight in some sense. Furthermore, we prove that for all and , and if is a prime power, then the equality holds. 相似文献
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Let and be positive integers with . Given a permutation of integers , we consider -consecutive sums of , i.e., for , where we let . What we want to do in this paper is to know the exact value of where denotes the set of all permutations of . In this paper, we determine the exact values of for some particular cases of and . As a corollary of the results, we obtain , and for any . 相似文献
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《Discrete Mathematics》2022,345(12):113077
In 2020, Bennett, Carrillo, Machacek and Sagan gave a polynomial generalization of the Narayana numbers and conjectured that these polynomials have positive integer coefficients for and for . In 2020, Sagan and Tirrell used a powerful algebraic method to prove this conjecture (in fact, they extend and prove the conjecture for more than just the type A case). In this paper we give a combinatorial proof of a formula satisfied by the Lucas-Narayana polynomials described by Bennett et al. This gives a combinatorial proof that these polynomials have positive integer coefficients. A corollary of our main result establishes a parallel theorem for the FiboNarayana numbers , providing a combinatorial proof of the conjecture that these are positive integers for . 相似文献
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In 1996, Cox and Rodger [Cycle systems of the line graph of the complete graph, J. Graph Theory 21 (1996) 173–182] raised the following question: For what values of and does there exist an -cycle decomposition of In this paper, the above question is answered for In fact, it is shown that the -fold line graph of the complete graph has a -decomposition if and only if and 相似文献
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Brualdi and Hollingsworth conjectured in Brualdi and Hollingsworth (1996) that in any complete graph , , which is properly colored with colors, the edge set can be partitioned into edge disjoint rainbow spanning trees (where a graph is said to be rainbow if its edges have distinct colors). Constantine (2002) strengthened this conjecture asking the rainbow spanning trees to be pairwise isomorphic. He also showed an example satisfying his conjecture for every . Caughmann, Krussel and Mahoney (2017) recently showed a first infinite family of edge colorings for which the conjecture of Brualdi and Hollingsworth can be verified. In the present paper, we extend this result to all edge-colorings arising from cyclic 1-factorizations of constructed by Hartman and Rosa (1985). Finally, we remark that our constructions permit to extend Constatine’s result also to all . 相似文献
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We provide a complete spectral analysis of all self-adjoint operators acting on which are associated with two doubly infinite Jacobi matrices with entries given by and respectively, where and . As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson q-Bessel function. 相似文献
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《Indagationes Mathematicae》2019,30(6):1079-1086
Let be a nonzero integer. A set of nonzero integers such that is a perfect square for all is called a --tuple. In this paper, we consider the question, for a given integer which is not a perfect square, how large and how small can be the largest element in a -quadruple. We construct families of -quadruples in which the largest element is of order of magnitude , resp. . 相似文献
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Let be the -color Ramsey number of an odd cycle of length . It is shown that for each fixed , for all sufficiently large , where is a constant. This improves an old result by Bondy and Erd?s (1973). 相似文献
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Judit Abardia-Evéquoz Károly J. Böröczky Mátyás Domokos Dávid Kertész 《Journal of Functional Analysis》2019,276(11):3325-3362
The space of continuous, -equivariant, , and translation covariant valuations taking values in the space of real symmetric tensors on of rank is completely described. The classification involves the moment tensor valuation for and is analogous to the known classification of the corresponding tensor valuations that are -equivariant, although the method of proof cannot be adapted. 相似文献
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《Discrete Mathematics》2022,345(5):112801
Let G and H be simple graphs. The Ramsey number is the minimum integer N such that any red-blue-coloring of edges of contains either a red copy of G or a blue copy of H. Let denote m vertex-disjoint copies of . A lower bound is that . Burr, Erd?s and Spencer proved that this bound is indeed the Ramsey number for , and . In this paper, we show that this bound is the Ramsey number for and . We also show that this bound is the Ramsey number for and . 相似文献
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Let be a simple connected graph with vertices and edges. The spectral radius of is the largest eigenvalue of its adjacency matrix. In this paper, we firstly consider the effect on the spectral radius of a graph by removing a vertex, and then as an application of the result, we obtain a new sharp upper bound of which improves some known bounds: If , where is an integer, then The equality holds if and only if is a complete graph or , where is the graph obtained from by deleting some edge . 相似文献
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Qichun Wang 《Discrete Mathematics》2019,342(12):111625
It was proved by J. Schatz that the covering radius of the second order Reed–Muller code is 18 (Schatz (1981)). However, the covering radius of has been an open problem for many years. In this paper, we prove that the covering radius of is 40, which is the same as the covering radius of in . As a corollary, we also find new upper bounds for the covering radius of , . 相似文献
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《Discrete Mathematics》2019,342(5):1275-1292
A discrete function of variables is a mapping , where , and are arbitrary finite sets. Function is called separable if there exist functions for , such that for every input the function takes one of the values . Given a discrete function , it is an interesting problem to ask whether is separable or not. Although this seems to be a very basic problem concerning discrete functions, the complexity of recognition of separable discrete functions of variables is known only for . In this paper we will show that a slightly more general recognition problem, when is not fully but only partially defined, is NP-complete for . We will then use this result to show that the recognition of fully defined separable discrete functions is NP-complete for .The general recognition problem contains the above mentioned special case for . This case is well-studied in the context of game theory, where (separable) discrete functions of variables are referred to as (assignable) -person game forms. There is a known sufficient condition for assignability (separability) of two-person game forms (discrete functions of two variables) called (weak) total tightness of a game form. This property can be tested in polynomial time, and can be easily generalized both to higher dimension and to partially defined functions. We will prove in this paper that weak total tightness implies separability for (partially defined) discrete functions of variables for any , thus generalizing the above result known for . Our proof is constructive. Using a graph-based discrete algorithm we show how for a given weakly totally tight (partially defined) discrete function of variables one can construct separating functions in polynomial time with respect to the size of the input function. 相似文献
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Let be an array of nonnegative numbers satisfying the recurrence relation with and unless . In this paper, we first prove that the array can be generated by some context-free Grammars, which gives a unified proof of many known results. Furthermore, we present criteria for real rootedness of row-generating functions and asymptotical normality of rows of . Applying the criteria to some arrays related to tree-like tableaux, interior and left peaks, alternating runs, flag descent numbers of group of type , and so on, we get many results in a unified manner. Additionally, we also obtain the continued fraction expansions for generating functions related to above examples. As results, we prove the strong -log-convexity of some generating functions. 相似文献
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《Discrete Mathematics》2021,344(12):112600
An -colored-mixed graph is a graph having m colors of arcs and n colors of edges. We do not allow two arcs or edges to have the same endpoints. A homomorphism from an -colored-mixed graph G to another -colored-mixed graph H is a morphism such that each edge (resp. arc) of G is mapped to an edge (resp. arc) of H of the same color (and orientation). An -colored-mixed graph T is said to be -universal if every graph in (the planar -colored-mixed graphs with girth at least g) admits a homomorphism to T.We show that planar -universal graphs do not exist for (and any value of g) and find a minimal (in the number vertices) planar -universal graphs in the other cases. 相似文献