Báo cáo toán học: "RSK Insertion for Set Partitions and Diagram Algebras" pps

... combinatorics 11(2) (2005), #R24 3 RSK Insertion for Set Partitions and Diagram Algebras Tom Halverson ∗ and Tim Lewandowski ∗ Department of Mathematics and Computer Science Macalester College, ... insertion of Brauer diagrams (matchings). Dulucq and Sagan [DS] extend this insertion to work for partial matchings (and other generalizations for skew oscillating tablea...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:21

... Dordrecht-Holland / Boston-U.S.A., 1974. 4. L. Moser and M. Wyman, An asymptotic for the Bell numbers,Trans.Roy.Soc.Can.49 (1955), 49–54. 5. B. Pittel, Random set partitions: asymptotics of subset counts,J.Comb.Theory,A79 ... between n and n/ log n does not seem to be sufficiently large to account for such a sharp contrast with the uniform partitions. Acknowledgement. I am indebted...

Ngày tải lên: 07/08/2014, 06:20

... e(H)=|I|,andtheweight is the number of incidences between vertices and edges i(H)=  i∈I |H i |. We write [a, b] for the interval a ≤ x ≤ b, x ∈ N ,and[ k ]for[ 1,k]. If X, Y ⊂ N and x<yfor all x ... [y t  −1 ,y t  − 1] and z 2 ≥ y t  . Z is unique for t  ≥ 4andfort  = 3 we take the Z with the largest middle element. We distinguish the cases t  = 3 and t  ≥ 4. For t...

Ngày tải lên: 07/08/2014, 06:20

... x j = 0 for some j ∈ {1, 2, . . . , t}. Let a k = |V k |, a j = |V j | and  = x k a j a k /(a j + a k ). Define a new weighting x  by x  v = x v for v ∈ V \(V k ∪ V j ), x  v = /a j for v ... x v for v ∈ V \(V k ∪ V j ), x  v = /a j for v ∈ V j and x  v = x k − /a k for v ∈ V k . It is straightforward to check that x  ∈ S p and λ(G, x  ) > λ(G, x), co...

Ngày tải lên: 07/08/2014, 15:23

... undirected, and simple. The vertex set and edge s et of a graph G are denoted by V (G) and E(G). For vertices v, w ∈ V (G), we write v ∼ w if vw ∈ E(G), and v ∼ w if vw ∈ E(G). For S ⊆ V (G), ... G ∗ ∼ = P D+1 and for some k ∈ [2, D − 1], the vertices u ∗ k−1 and u ∗ k+1 of G ∗ are both not of type (1). Then u ∗ k−1 and u ∗ k+1 are both of type (N). Proof. Let x and...

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Ngày tải lên: 05/08/2014, 15:21

... I k and I k = I k for all k ≥ 1. Let R[It]=  k≥0 I k t k be the Rees algebra of I.Itisknown that R[It] is normal if and only if I k = I k for all k ≥ 1. Therefore, combining Theorem 2.1 and ... multiset consisting of c i copies of i for i =1, , n. Thus, a subset C ⊆ V corresponds to an (0,1)-vector c with c i =1ifi ∈ C and c i =0ifi ∈ C ,and C is a vertex cover of Δ if  i∈F...

Ngày tải lên: 06/08/2014, 05:20

... Banderier and Flajolet [2], and P´olya-Eggenberger urn models, see Flajolet et al. [3, 4], and Hwang et al. [6]. For the weighted lattice paths and absorbing lines studied, we obtain closed formulæ ... N 0 } and the set of absorbing states by A = {(tm + s, m) | m ∈ N 0 }. Figure 1: Sample paths for absorption at x = 0, y = x and y = x/2. 1.3 Motivation and related work The...

Ngày tải lên: 07/08/2014, 21:21