共查询到20条相似文献,搜索用时 93 毫秒
1.
Let , be independent and identically distributed random variables with values in . We transform (‘prune’) the sequence , of discrete random samples into a sequence , of contiguous random sets by replacing with if . We consider the asymptotic behaviour of as . Applications include path growth in digital search trees and the number of tables in Pitmanʼs Chinese restaurant process if the latter is conditioned on its limit value. 相似文献
2.
Let and be two independent sequences of iid Bernoulli random variables with parameter 1/2. Let be the length of the longest increasing sequence which is a subsequence of both finite sequences and . We prove that, as n goes to infinity, converges in law to a Brownian functional that we identify. To cite this article: C. Houdré et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
3.
Partitioning a set into similar, if not, identical, parts is a fundamental research topic in combinatorics. The question of partitioning the integers in various ways has been considered throughout history. Given a set of integers where , let the gap sequence of this set be the unordered multiset . This paper addresses the following question, which was explicitly asked by Nakamigawa: can the set of integers be partitioned into sets with the same gap sequence? The question is known to be true for any set where the gap sequence has length at most two. This paper provides evidence that the question is true when the gap sequence has length three. Namely, we prove that given positive integers and , there is a positive integer such that for all , the set of integers can be partitioned into 4-sets with gap sequence , . 相似文献
4.
5.
The conservative number of a graph is the minimum positive integer , such that admits an orientation and a labeling of its edges by distinct integers in , such that at each vertex of degree at least three, the sum of the labels on the in-coming edges is equal to the sum of the labels on the out-going edges. A graph is conservative if . It is worth noting that determining whether certain biregular graphs are conservative is equivalent to find integer Heffter arrays.In this work we show that the conservative number of a galaxy (a disjoint union of stars) of size is for , , and otherwise. Consequently, given positive integers , , …, with for , we construct a cyclic -cycle system of infinitely many circulant graphs, generalizing a result of Bryant, Gavlas and Ling (2003). In particular, it allows us to construct a cyclic -cycle system of the complete graph , where . Also, we prove necessary and sufficient conditions for the existence of a cyclic -cycle system of , where is a 1-factor. Furthermore, we give a sufficient condition for a subset of to be sequenceable. 相似文献
6.
Sergey V. Astashkin Pavel A. Terekhin 《Journal of Mathematical Analysis and Applications》2018,457(1):645-671
Let be a mean zero function and let , , be the dyadic dilations and translations of f. We investigate conditions on f, under which the linear operator defined by , , where , , are mean zero Haar functions, can be continuously extended to the closed linear span in a certain function space X. Among other results we prove that is bounded in every symmetric space with nontrivial Boyd indices whenever and f has “good” Haar spectral properties. In the special case of so-called Haar chaoses the above results can be essentially refined and sharpened. In particular, we find necessary and sufficient conditions, under which the operator , generated by a Haar chaos f of order 1, is continuously invertible in for all . 相似文献
7.
8.
9.
10.
11.
Elena Rubei 《Discrete Mathematics》2012,312(19):2872-2880
12.
13.
14.
《Discrete Mathematics》2007,307(17-18):2217-2225
15.
16.
Let e be a positive integer, p be an odd prime, , and be the finite field of q elements. Let . The graph is a bipartite graph with vertex partitions and , and edges defined as follows: a vertex is adjacent to a vertex if and only if and . If and , the graph contains no cycles of length less than eight and is edge-transitive. Motivated by certain questions in extremal graph theory and finite geometry, people search for examples of graphs containing no cycles of length less than eight and not isomorphic to the graph , even without requiring them to be edge-transitive. So far, no such graphs have been found. It was conjectured that if both f and g are monomials, then no such graphs exist. In this paper we prove the conjecture. 相似文献
17.
18.
D. Buraczewski E. Damek J. Zienkiewicz 《Stochastic Processes and their Applications》2018,128(9):2923-2951
We consider first passage times for the perpetuity sequence where are i.i.d. random variables with values in . Recently, a number of limit theorems related to were proved including the law of large numbers, the central limit theorem and large deviations theorems (see Buraczewski et al., in press). We obtain a precise asymptotics of the sequence , , which considerably improves the previous results of Buraczewski et al. (in press). There, probabilities were identified, for some large intervals around , with lengths growing at least as . Remarkable analogies and differences to random walks (Buraczewski and Ma?lanka, in press; Lalley, 1984) are discussed. 相似文献
19.
20.
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