共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
3.
6.
7.
We consider four classes of polynomials over the fields , , , , , , , where . We find sufficient conditions on the pairs for which these polynomials permute and we give lower bounds on the number of such pairs. 相似文献
8.
9.
In this paper, we generalize the notion of functional graph. Specifically, given an equation with variables X and Y over a finite field of odd characteristic, we define a digraph by choosing the elements in as vertices and drawing an edge from x to y if and only if . We call this graph as equational graph. In this paper, we study the equational graph when choosing with a polynomial over and λ a non-square element in . We show that if f is a permutation polynomial over , then every connected component of the graph has a Hamiltonian cycle. Moreover, these Hamiltonian cycles can be used to construct balancing binary sequences. By making computations for permutation polynomials f of low degree, it appears that almost all these graphs are strongly connected, and there are many Hamiltonian cycles in such a graph if it is connected. 相似文献
10.
Let M be a random rank-r matrix over the binary field , and let be its Hamming weight, that is, the number of nonzero entries of M.We prove that, as with r fixed and tending to a constant, we have that converges in distribution to a standard normal random variable. 相似文献
11.
12.
In this paper, we establish a new asymptotic expansion of Gurland's ratio of gamma functions, that is, as ,where with and , , are the Bernoulli polynomials. Using a double inequality for hyperbolic functions, we prove that the function is completely monotonic on if , which yields a sharp upper bound for . This shows that the approximation for Gurland's ratio by the truncation of the above asymptotic expansion has a very high accuracy. We also present sharp lower and upper bounds for Gurland's ratio in terms of the partial sum of hypergeometric series. Moreover, some known results are contained in our results when . 相似文献
13.
14.
15.
16.
17.
18.
19.
20.
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