Báo cáo toán học: "On the Stanley-Wilf conjecture for the number of permutations avoiding a given pattern" ppt

... a given pattern Richard Arratia Department of Mathematics University of Southern California Los Angeles, CA 90089-1113 email: rarratia@math.usc.edu Submitted: July 27, 1999; Accepted: August 25, ... 1999. Abstract. Consider, for a permutation σ ∈S k ,thenumberF(n, σ) of permuta- tions in S n which avoid σ as a subpattern. The conjecture of Stanley and Wilf is that for...

Ngày tải lên: 07/08/2014, 06:22

... locality The locality of a tree representation such as the Pr¨ufer Code is a measure of the regularity of the mapping between the tree space and the string space (i.e., T n and P n , in the case of ... analysis preceding Theorem 2.) The fitted polynomials gave the exact value of N(µ, n, ∆) for every value of n considered, and in every case, the number o...

Ngày tải lên: 07/08/2014, 15:22

... (16). Analyzing the abelianization map ab : T → S (the map making the variables x commute), Ro sas and Sagan [15, Thm. 2.1] show that ab| N satisfies: ab(m A ) = λ (A) ! m λ (A) . (19) In particular, ... partitions of [n] and permutations σ : [n] → [n] are transferred in a natural way to permutations Par[σ]: Par[n] → Par[n]. The number fix Par[σ] of fixed points of this...

Ngày tải lên: 08/08/2014, 12:23

... on small on-line Ramsey numbers for paths and their generalization, Australasian J. Combinatorics, 40 (2008), 27–36. [22] P. Pralat, A note on off-diagonal small on-line Ramsey numbers for paths, ... is a monochromatic weighted claw with capacity a at the center and capacities b, c, d at the leaves. Similarly, an (a, b, c)-triangle is a monochromatic weighted triangle with cap...

Ngày tải lên: 08/08/2014, 14:23

... numbers for small graphs, Utilitas Mathematica 49 (1996) 85–96. [2] Clapham C.R.J., Flockhart A. , Sheehan J.: Graphs without four-cycles, Journal of Graph Theory 13 (1989) 29–47 . [3] Faudree ... on some Ramsey numbers involving quadrilateral, Ars Combinatoria 90 (2009) 337–344. the electronic journal of combinatorics 18 (2011), #P154 5 for each v ∈ V (G), the number of edge...

Ngày tải lên: 08/08/2014, 14:23

... Vietnam Journal of Mathematics 33:1 (2005) 9–17 Using Boundary-Operator Method for Approximate Solution of a Boundary Value Problem (BVP) for Triharmonic Equation * Dang Quang A Hanoi Institute of ... is the solution of the equation (8) - (10) uniquely defines a function u which is the solution of the Problem (1) such that the relation (7) is valid. Proof. The P...

Ngày tải lên: 06/08/2014, 05:20

... finds a matching for D r that is only about half the size of a maximum matching [13] . This performance is as poor as that of any procedure that finds a maximal matching. On the other hand, there are ... values of n and m. The theorem states that the greedy procedure finds a matching of size at least k max . Given only n and m, no algorithm can be guaranteed to find a...

Ngày tải lên: 07/08/2014, 06:20

... trees rather than the number of rooted trees, one has to apply Otter’s theorem [7, 18] that states that the number of representations of a tree as a rooted tree equals one plus the number of representations ... extends the aforementioned results, and in recent years a wealth of literature on the so-called extremal problem (given a class of graphs, determin...

Ngày tải lên: 08/08/2014, 01:20

... will de- note the set of standard Catalan trees by standard(C) and the set of standard marked Catalan trees by standard(C, ∗). The standard trees in C 4 are , , , , . One of the standard trees in ... have numerical evidence to suggest that the ratio of the number of k-bad standard binary trees in B p to the total number of standard trees in B p decreases the el...

Ngày tải lên: 07/08/2014, 06:22