共查询到20条相似文献,搜索用时 328 毫秒
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Let be the number of numerical semigroups of genus . We present an approach to compute by using even gaps, and the question: Is it true that ? is investigated. Let be the number of numerical semigroups of genus whose number of even gaps equals . We show that for and for ; thus the question above is true provided that for . We also show that coincides with , the number introduced by Bras-Amorós (2012) in connection with semigroup-closed sets. Finally, the stronger possibility arises being the golden number. 相似文献
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Stefan Steinerberger 《Indagationes Mathematicae》2018,29(5):1167-1178
A sequence on the torus is said to exhibit Poissonian pair correlation if the local gaps behave like the spacings of a Poisson random variable, i.e. We show that being close to Poissonian pair correlation for few values of is enough to deduce global regularity statements: if, for some , a set of points satisfies then the discrepancy of the set satisfies . We also show that distribution properties are reflected in the global deviation from the Poissonian pair correlation where the lower bound is conditioned on . The proofs use a connection between exponential sums, the heat kernel on
and spatial localization. Exponential sum estimates are obtained as a byproduct. We also describe a connection to diaphony and several open problems. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2007,66(1):241-252
Let and be the critical Sobolev–Hardy exponents. Via variational methods and the analytic technique, we prove the existence of a nontrivial solution to the singular semilinear problem , for and suitable functions . 相似文献
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Let and be a sufficiently large real number. In this paper, we prove that, for almost all , the Diophantine inequality is solvable in primes . Moreover, we also investigate the problem of six primes and prove that the Diophantine inequality is solvable in primes for sufficiently large real number . 相似文献
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This paper deals with the following nonlinear elliptic equation where , is a bounded non-negative function in . By combining a finite reduction argument and local Pohozaev type of identities, we prove that if and has a stable critical point with and , then the above problem has infinitely many solutions. This paper overcomes the difficulty appearing in using the standard reduction method to locate the concentrating points of the solutions. 相似文献
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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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This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of points has non-crossing spanning trees and non-crossing forests. This improves the previous lower bounds on the maximum number of non-crossing spanning trees and of non-crossing forests among all sets of points in general position given by Dumitrescu, Schulz, Sheffer and Tóth (2013). Our analysis relies on the tools of analytic combinatorics, which enable us to count certain families of forests on points in convex position, and to estimate their average number of components. A new upper bound of for the number of non-crossing spanning trees of the double chain is also obtained. 相似文献
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Antal Joós 《Discrete Mathematics》2018,341(9):2544-2552
It is known that . In 1968, Meir and Moser (1968) asked for finding the smallest such that all the rectangles of sizes , , can be packed into a square or a rectangle of area . First we show that in Paulhus (1997), the key lemma, as a statement, in the proof of the smallest published upper bound of the minimum area is false, then we prove a different new upper bound. We show that if the rectangles are packed into a square and if the rectangles are packed into a rectangle. 相似文献
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《Discrete Mathematics》2018,341(10):2708-2719