Báo cáo toán học: "Counting nondecreasing integer sequences that lie below a barrier Robin Pemantle" ppt

... explicit formula (Proctor, 1988, p.320). A relatively easy bivariate recursion, d ecompos- ing all sequences according to n and a n , leads to a bivariate generating function, then a univariate generating ... in the formal power series ring, it is necessary, as is indeed that case, that there be only finitely many summands for each monomal x k . One may ask whether in fact (4) ho...

Ngày tải lên: 07/08/2014, 21:21

... If p a contains more than one vertex (say p a = a, a 2 , a 3 , . . . , a n ), then (a, a 2 ) is lonely since p a is a path in L C (G). But {a} is a singleton color class, so (a 2 , a) is also lonely. ... z 1 ∈ d  i=1 N i giving a final contradiction. Proof of Theorem A. Assume (to reach a contradiction) that G satisfies χ ≥ ∆ ≥ 6 and does not contain a K ∆ . Witho...

Ngày tải lên: 07/08/2014, 15:22

... N d (T) was calculated in [CGG] in a spirit similar to the above computation, but it was mistakenly assumed that M ≤n (T ) β n−1 N(T ), rendering their bound invalid. Our second method eliminates ... the Riemann ξ-function, but the manipulations work equally well for any function such that it and all of its derivatives have the same number of zeros. We write f(T ) g(T )forf(T) ≥ g(T )+o...

Ngày tải lên: 07/08/2014, 06:20

... inverses; so the Tsaranov group is an invariant of the switching class, that is, of the two-graph. Now Seidel and Tsaranov [10] showed that the Tsaranov group of the two-graph obtained from a tree T by ... classes; and replacing a point by an equivalent point does not a ect membership in V (that is, ≡ is a congruence). Thus we have a ‘canonical projection’ onto a reduced two-g...

Ngày tải lên: 07/08/2014, 06:20

... and (ii). Graphs are (not necessarily simple) hypergraphs satisfying (i). Partitions are simple hypergraphs satisfying (ii). A pattern is any k-permutation p = a 1 a 2 a k of [k]. We associate ... for any fixed number of logarithms. 3 The conjectures C1–C6 hold for A- patterns and inverse V-patterns A k-permutation p = a 1 a 2 a k is a V-pattern if, for some i, a 1 a 2...

Ngày tải lên: 07/08/2014, 06:20

... yield path counts related to the Narayana polynomials. Mathematical Reviews Subject Classification: 0 5A1 5 Key words: Lattice paths, Narayana numbers, Delannoy numbers. 1 Introduction In the plane ... Paths by Narayana Polynomials Robert A. Sulanke Boise State University Boise, Idaho, USA <sulanke@math.boisestate.edu> Submitted: April 15, 2000; Accepted: August 3, 2000 Abstract Let d(n...

Ngày tải lên: 07/08/2014, 06:20

... Laflamme ∗ Department of Mathematics and Statistics University of Calgary, Calgary, Alberta, Canada T2N 1N4 email: laf@math.ucalgary.ca Istv´an Szalkai † Department of Mathematics and Computer Science University ... A 1 =[1,0] ,A 2 =[0,1] ,A 3 =[1,1] and A 4 =[1,2], using the “base” {C,O} in 2 . The vector set H = {A 1 ,A 2 ,A 3 ,A 4 } contains the simplexes {A 1 ,A 2 ,A 3 }...

Ngày tải lên: 07/08/2014, 06:22

... [CGHK78] to enumerate permutations avoiding all pairs of a pattern of length 3 and a pattern of length 4. Recently, Albert et al. [AAA + 03] enumerated {1324, 31524}-avoiding permuta- tions, while ... n-th Catalan number, a classical sequence [Sta99]. When τ is of length 4, it has been shown that the only essentially different patterns are 1234, 1342 and 1324; all other patterns of len...

Ngày tải lên: 07/08/2014, 07:21

... between sparse partitions and sparse words. We say that awordu = a 1 a 2 a l over an alphabet A, |A| = r,isk-sparse if a i = a j , j>i, implies j − i ≥ k. (We remark that k-sparse words are basic ... 237–243. [6] P. Flajolet and R. Sedgewick, Analytic Combinatorics, available at http://pauillac.inria.fr/algo/flajolet/Publications/books.html [7] M. Klazar, Generalized Davenpo...

Ngày tải lên: 07/08/2014, 08:22

... 1011121314151617181920212223 1 2 3 0 u = a 1 ¯aaa¯aaβ 2 β 1 a a 1 a 2 aa a a ¯aaβ 1 a 1 Figure 1: A 2-colored Motzkin path and its corresponding word Throughout this paper we denote by M the set of all k-colored ... rise). Obviously, a point of a k-colored Motzkin path is a peak (resp. valley) if and only if it is both left and right peak (resp. valley). The right peak and...

Ngày tải lên: 07/08/2014, 08:22