共查询到20条相似文献,搜索用时 575 毫秒
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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
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Let be an algebraically closed field of characteristic 0, and a Cohen–Macaulay graded domain with . If A is semi-standard graded (i.e., A is finitely generated as a -module), it has the h-vector, which encodes the Hilbert function of A. From now on, assume that . It is known that if A is standard graded (i.e., ), then A is level. We will show that, in the semi-standard case, if A is not level, then divides . Conversely, for any positive integers h and n, there is a non-level A with the h-vector . Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings). 相似文献
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In 1965 Erd?s introduced : is the smallest integer such that every is the sum of s distinct primes or squares of primes where a prime and its square are not both used. We prove that for all sufficiently large s, , and the set of s with the equality has the density 1. 相似文献
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Elena Rubei 《Discrete Mathematics》2012,312(19):2872-2880
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《Discrete Mathematics》2007,307(7-8):916-922
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《Nonlinear Analysis: Real World Applications》2007,8(2):435-446
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear discrete state dependent delays predator–prey systemwhere are positive -periodic, is a fixed positive integer. are -periodic and . are -periodic with respect to their first arguments, respectively. are positive constants. 相似文献
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For bipartite graphs , the bipartite Ramsey number is the least positive integer so that any coloring of the edges of with colors will result in a copy of in the th color for some . In this paper, our main focus will be to bound the following numbers: and for all for and for Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result. 相似文献
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Neil J.Y. Fan Peter L. Guo Grace L.D. Zhang 《Journal of Pure and Applied Algebra》2017,221(1):237-250
Parabolic R-polynomials were introduced by Deodhar as parabolic analogues of ordinary R-polynomials defined by Kazhdan and Lusztig. In this paper, we are concerned with the computation of parabolic R-polynomials for the symmetric group. Let be the symmetric group on , and let be the generating set of , where for , is the adjacent transposition. For a subset , let be the parabolic subgroup generated by J, and let be the set of minimal coset representatives for . For in the Bruhat order and , let denote the parabolic R-polynomial indexed by u and v. Brenti found a formula for when , and obtained an expression for when . In this paper, we provide a formula for , where and i appears after in v. It should be noted that the condition that i appears after in v is equivalent to that v is a permutation in . We also pose a conjecture for , where with and v is a permutation in . 相似文献
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Haïm Brezis Petru Mironescu 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(5):1355-1376
We investigate the validity of the Gagliardo–Nirenberg type inequality
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with . Here, are non negative numbers (not necessarily integers), , and we assume the standard relationsBy the seminal contributions of E. Gagliardo and L. Nirenberg, (1) holds when are integers. It turns out that (1) holds for “most” of values of , but not for all of them. We present an explicit condition on which allows to decide whether (1) holds or fails. 相似文献