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Balázs Gerencsér 《Stochastic Processes and their Applications》2019,129(9):3570-3584
The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square to approach a stationary distribution with density proportional to for with some large parameter .Diaconis conjectured the mixing time of this process to be which we confirm in this paper. This improves on the currently known estimate. 相似文献
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Lionel Nguyen Van Thé 《Expositiones Mathematicae》2019,37(2):192-199
Say that a graph is representable in if there is a map from its vertex set into the Euclidean space such that iff and are both edges or both non-edges in . The purpose of this note is to present the proof of the following result, due to Einhorn and Schoenberg in Einhorn and Schoenberg (1966): if finite is neither complete nor independent, then it is representable in . A similar result also holds in the case of finite complete edge-colored graphs. 相似文献
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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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After a brief review of the existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then focus on PBs of of the form , where n and d are positive integers and . Our contributions include two nonexistence results: (1) If q is even and sufficiently large and , then is not a PB of . (2) If , q is sufficiently large and , then is not a PB of under certain additional conditions. (1) partially confirms a recent conjecture by Tu et al. (2) is an extension of a previous result with . 相似文献
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In this paper, several classes of complete permutation polynomials with the form over are proposed by the AGW criterion and determining the number of solutions of some equations. Our results also enrich constructions of known permutation polynomials. 相似文献
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We investigate a sharp Moser–Trudinger inequality which involves the anisotropic Dirichlet norm on for . Here F is convex and homogeneous of degree 1, and its polar represents a Finsler metric on . Under this anisotropic Dirichlet norm, we establish the Lions type concentration-compactness alternative. Then by using a blow-up procedure, we obtain the existence of extremal functions for this sharp geometric inequality. 相似文献
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n-to-1 mappings have wide applications in many areas, especially in cryptography, finite geometry, coding theory and combinatorial design. In this paper, many classes of n-to-1 mappings over finite fields are studied. First, we provide a characterization of general n-to-1 mappings over by means of the Walsh transform. Then, we completely determine 3-to-1 polynomials with degree no more than 4 over . Furthermore, we obtain an AGW-like criterion for characterizing some close relationship between the n-to-1 property of a mapping over finite set A and that of another mapping over a subset of A. Finally, we apply the AGW-like criterion into several forms of polynomials and obtain some explicit n-to-1 mappings. Especially, three explicit constructions of the form from the cyclotomic perspective, and several classes of n-to-1 mappings of the form are provided. 相似文献
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Let q be a perfect power of a prime number p and be an elliptic curve over given by the equation . For a positive integer n we denote by the number of rational points on E (including infinity) over the extension . Under a mild technical condition, we show that the sequence contains at most 10200 perfect squares. If the mild condition is not satisfied, then is a perfect square for infinitely many n including all the multiples of 12. Our proof uses a quantitative version of the Subspace Theorem. We also find all the perfect squares for all such sequences in the range and . 相似文献
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