Báo cáo toán học: "Growth rates for subclasses of Av(321)" ppsx

... each element of λ i is labeled with the largest label of an element of λ i−1 of smaller value. • For odd i > 1, each element of λ i is labeled with the largest label of an element of λ i−1 to ... tight for M(I n , I m ). For the remainder of this paper we will only be using the second of these estimates; that the growth rate of a bounded merge of two permutation...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 10:20

... the i-th column of the Ferrars graph of π.TheDurfee square of π is the largest square subarray of dots in the Ferrars graph of π.Letd(π)denotethesize(numberofrows)oftheDurfeesquareof π. The sequence (π 1 − ... π d(π) −π  d(π) ) isthesequenceofsuccessive ranks of π [At]. It will be convenient to work with the negatives of the ranks, so, for 1 ≤ i ≤ d(π), let r i (π)=π  i −π i...

Ngày tải lên: 07/08/2014, 06:20

... periods of A are the positions of the ones in AA. With each non-zero period p, there is a corresponding prefix a 0 a p−1 of A. Call B a base of A if B = a 0 a p−1 for some period p> 0of A. For ... and 4.6, for any D with no A-factor, there exist a Gray code for H(m + p; D) between two strings independent of D and of equal parity. This satisfies condition (2) of Lemma...

Ngày tải lên: 07/08/2014, 06:20

... limitations of our approach. We thank Donatella Merlini and Renzo Sprugnoli for helpful conversations. 2. A Limit Theorem for Products of Powers Let ZZ denote the integers. For a set V of vectors, ... denotes the coefficient of the monomial x n in the power series h(x). We obtained asymptotics for g n from (2) for some types of formal power series [6]. When f has a nonzero r...

Ngày tải lên: 07/08/2014, 06:20

... vectors for the sequences discovered by Lunnon. No proof of Theorem 2.2 will be given because the proof of Theorem 2.2 is ex- tremely similar to the proof of Theorem 2.1 given below. 3 Proof of Theorem ... the structure of w t . By property (i) of w t , we have w t (i)=v(i) for i ≥ t. It is also clear from the definition of w t that w t (i)= 0for i<t−b(t). So, the interes...

Ngày tải lên: 07/08/2014, 06:22

... Then, for all i ∈ [n]     v 1 (i) − 1 √ n      c log n log np 1 √ n ∆ with high probability, for some constant c. 3 Proofs 3.1 The First Proof In this section we present the first proof of ... as in th e proof of Theore m 14. Assume th at λ 1  d and that the root of T 1 is vertex 1. Let, u = γ 1 v 1 (A) such that u(1) = 1. Then, for all r  l (l is de fined in the proof o...

Ngày tải lên: 08/08/2014, 01:20

... terms of lower shadows, and initial segments in the colex order, defined for finite subsets of N by A ≺ C B if max(A  B) ∈ B. The two forms are equivalent by a double reversal: complementation of ... and write i(G; ¯x) for the number of independent sets in G not containing x. Similarly, if G is a graph, and x and y are vertices of G, we write i(G; x, ¯y) for the number of ind...

Ngày tải lên: 08/08/2014, 14:23

... ordinary marker for the length of the string and x i marks the occurrence of symbol i. See [RY,§2] for a proof. Proposition 3.2. Let D n (z, x 1 , ,x n ) be the generating series of sequences on ... is equal to the number of sequences over {0, 1, 2, 3} of length n with n − l(α) occurrences of 0, m 1 (α) occurrences of 1, m 2 (α) occurrences of 2 and one occurrence of 3 (...

Ngày tải lên: 07/08/2014, 06:20

... than the poset of graphs ordered by the operations of edge contraction and vertex deletion. (That this poset of graphs does not contain an infinite antichain is a famous theorem of Robertson and ... Infinite Antichain of Permutations Daniel A. Spielman Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139 spielman@math.mit.edu Mikl´os B´ona Department...

Ngày tải lên: 07/08/2014, 06:20