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Let denote the finite field of order q of characteristic p. We study the p-adic valuations for zeros of L-functions associated with exponential sums of the following family of Laurent polynomials where , . When , the estimate of the associated exponential sum appears in Iwaniecʼs work on small eigenvalues of the Laplace–Beltrami operator acting on automorphic functions with respect to the group , and Adolphson and Sperber gave complex absolute values for zeros of the corresponding L-function. Using the decomposition theory of Wan, we determine the generic Newton polygon (q-adic values of the reciprocal zeros) of the L-function. Working on the chain level version of Dworkʼs trace formula and using Wanʼs decomposition theory, we are able to give an explicit Hasse polynomial for the generic Newton polygon in low dimensions, i.e., . 相似文献
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ParkChun-Gil 《数学物理学报(B辑英文版)》2005,25(3):449-454
It is shown that for a derivation f(x1o…oxj-1oxj 1o…xk)=k∑j=1x1o…oxu-1oxj 1o…oxkof(xj) on a JB*-algebra β, there exists a unique C-linear *-derivation D : β→β near the derivation. 相似文献
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Let be a prime power and be a positive integer. A subspace partition of , the vector space of dimension over , is a collection of subspaces of such that each nonzero vector of is contained in exactly one subspace in ; the multiset of dimensions of subspaces in is then called a Gaussian partition of . We say that contains a direct sum if there exist subspaces such that . In this paper, we study the problem of classifying the subspace partitions that contain a direct sum. In particular, given integers and with , our main theorem shows that if is a subspace partition of with subspaces of dimension for , then contains a direct sum when has a solution for some integers and belongs to the union of two natural intervals. The lower bound of captures all subspace partitions with dimensions in that are currently known to exist. Moreover, we show the existence of infinite classes of subspace partitions without a direct sum when or when the condition on the existence of a nonnegative integral solution is not satisfied. We further conjecture that this theorem can be extended to any number of distinct dimensions, where the number of subspaces in each dimension has appropriate bounds. These results offer further evidence of the natural combinatorial relationship between Gaussian and integer partitions (when ) as well as subspace and set partitions. 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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Let denote the graph on a vertices with edges between every pair of vertices. Take p copies of this graph , and join each pair of vertices in different copies with edges. The resulting graph is denoted by , a graph that was of particular interest to Bose and Shimamoto in their study of group divisible designs with two associate classes. The existence of z-cycle decompositions of this graph have been found when . In this paper we consider resolvable decompositions, finding necessary and sufficient conditions for a 4-cycle factorization of (when is even) or of minus a 1-factor (when is odd) whenever a is even. 相似文献
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We say a graph is -colorable with of ’s and of ’s if may be partitioned into independent sets and sets whose induced graphs have maximum degree at most . The maximum average degree, , of a graph is the maximum average degree over all subgraphs of . In this note, for nonnegative integers , we show that if , then is -colorable. 相似文献
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Let be a sequence of the Catalan-like numbers. We evaluate Hankel determinants and for arbitrary coefficients and . Our results unify many known results of Hankel determinant evaluations for classic combinatorial counting coefficients, including the Catalan, Motzkin and Schröder numbers. 相似文献
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For an algebraically closed field , we investigate a class of noncommutative -algebras called connected quantized Weyl algebras. Such an algebra has a PBW basis for a set of generators such that each pair satisfies a relation of the form , where and , with, in some sense, sufficiently many pairs for which . For such an algebra it turns out that there is a single parameter q such that each . Assuming that , we classify connected quantized Weyl algebras, showing that there are two types linear and cyclic. When q is not a root of unity we determine the prime spectra for each type. The linear case is the easier, although the result depends on the parity of n, and all prime ideals are completely prime. In the cyclic case, which can only occur if n is odd, there are prime ideals for which the factors have arbitrarily large Goldie rank.We apply connected quantized Weyl algebras to obtain presentations of two classes of quantum cluster algebras. Let be an odd integer. We present the quantum cluster algebra of a Dynkin quiver of type as a factor of a linear connected quantized Weyl algebra by an ideal generated by a central element. We also consider the quiver identified by Fordy and Marsh in their analysis of periodic quiver mutation. When n is odd, we show that the quantum cluster algebra of this quiver is generated by a cyclic connected quantized Weyl algebra in n variables and one further generator. We also present it as the factor of an iterated skew polynomial algebra in variables by an ideal generated by a central element. For both classes, the quantum cluster algebras are simple noetherian.We establish Poisson analogues of the results on prime ideals and quantum cluster algebras. We determine the Poisson prime spectra for the semiclassical limits of the linear and cyclic connected quantized Weyl algebras and show that, when n is odd, the cluster algebras of and are simple Poisson algebras that can each be presented as a Poisson factor of a polynomial algebra, with an appropriate Poisson bracket, by a principal ideal generated by a Poisson central element. 相似文献