Báo cáo toán học: "A note on the ranks of set-inclusion matrices" pps

... A note on the ranks of set-inclusion matrices D. de Caen Department of Mathematics and Statistics Queen’s University Kingston, Ontario, Canada K7L 3N6 decaen@mast.queensu.ca Submitted: ... relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1)-matr...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 05/08/2014, 15:21

... Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal of combinatorics 7 (2000), #R30 7 Proof. We need to show that the left-hand side of ... for many valuable com- ments. Due to their suggestions we were able to prove the main result of the note in its present sharp form. the electronic journal of combinator...

Ngày tải lên: 07/08/2014, 06:20

... bipartite digraphs, namely, specifying conditions on the cardinality of the edge-set of the digraph that guarantee the existence of a directed simple cycle of length at most four. As usual in Tur´an ... columns j =1, ,ρn.DenotebyM 4 the block consisting of the rows i = |A + |+1, ,mand the columns j =2ρn+1, ,n.DenotebyM 5 the block consisting of the rows i =1, ,...

Ngày tải lên: 07/08/2014, 06:23

... not strong and that no sets A and B satisfy the lemma. Let t be the number of strong components of T − v and let W i be the set of vertices in the i th strong component. If |W 1 |≥3, then choose a ... v 1 and all other arcs are of the form v i → v j with i<j. In other words, reversing the arc v n → v 1 gives the transitive tournament of order n. As noted by Moon [1]...

Ngày tải lên: 07/08/2014, 13:21

... vertices, which is the main result of the paper. The o r ganization of the paper is as follows. In the rest of this section we introduce basic notations. In Section 2, we verify the conjecture for ... is the intersection graph of a set I = {I 1 , . . . , I n } of intervals (arcs) on a circle C, i.e. if there exists a one-to-one correspondence between the vertices...

Ngày tải lên: 08/08/2014, 14:23

... the condition nP(|X 1 | > η n ) ≤ c(log n) ε 0 , 0 < ε 0 < 1 in theorem 1.1 of [12]. Remark 1.4. If EX 2 < ∞, then X is in the domain of attraction of the normal law. Therefore, the ... of random variables in the domain of attraction of the normal law, we will show that the ASCLT holds under a fairly general growth condition on d k = k −1 exp(ln k) α ),...

Ngày tải lên: 20/06/2014, 21:20

... row-span of this table. Since the dimension of the row-span of a matrix is equal to the dimension of its column-span, we can equally well study the dimension of the space spanned by the columns of the ... the reflection representation of a finite Coxeter group. This is essentially what we are looking at. (The defining representation of S n consists of the dir...

Ngày tải lên: 07/08/2014, 06:20

... (3) When conditioning on the event C P 0 , the random graphs of the resulting probability space may contain edges only from within the edges that connect vertices of different partitions of P 0 . The ... information on Maple) implementation of the downhill simplex function optimization method (see [13] for a good description of the method and a C implementation) to...

Ngày tải lên: 07/08/2014, 06:20

... bounded, then the height distribution concentrates on two consecutive points. 3 Derivation of Results We establish the five parts of Theorem 2. Since the analysis involves a routine use of the saddle ... of k. For purposes of comparison, we repeat these results below. Theorem 1 The distribution of the height of b-tries has the following asymptotic expan- sions for...

Ngày tải lên: 07/08/2014, 06:20