Báo cáo toán học: "Three-letter-pattern-avoiding permutations and functional equations" pot

... explicit determination of root systems and lattices involved. 5 Acknowledgements We thank Ed Assmus, Michel Deza, and Vladimir Tonchev for sending us their preprints and Chris Charnes, Slava Grishukhin ... paper R9. J.H. Conway , N.J.A. Sloane, Sphere Packings Lattices and Groups [SPLAG] J.H. Conway, N.J.A. Sloane, Sphere Packings Lattices and Groups, second edition, Springer Verlag...

Ngày tải lên: 07/08/2014, 06:20

... name “random knock-out tournaments.” A sequence (t 1 , ,t n ) represented a tournament of n rounds beginning with 1 +  t i players; in the first round 2t n players are paired off randomly and the ... have been called generating trees, and were introduced in [5]. They have been championed by J. West ([12],[13]), who has used them to study pattern-avoiding permutations, and by Barcucci et...

Ngày tải lên: 07/08/2014, 06:20

... result follows from the previous theorem and Theorem 1. References [1] Tofik Mansour and Alek Vainshtein, Restricted permutations, continued fractions and chebyshev polynomials, The Electronic ... interesting bijection between labeled trees and (132)-avoiding permutations. Problem 2. The number of lattice paths from (0, 0) to (n, n) with steps (1, 0) and (0, 1) that never rise abo...

Ngày tải lên: 07/08/2014, 06:20

... poset of rank n with ˆ 0and ˆ 1 and with rank function ρ. (See [29, Ch. 3] for poset terminology and notation used here.) Let S be a subset of [n − 1] = {1, 2, ,n−1}, and define α P (S)tobethenumberofchains ˆ 0= t 0 <t 1 <··· ... a<b<c<dand some block B of π contains both a and c,whilesomeblockB  of π contains both b and d,thenB= B  . We establish some connections...

Ngày tải lên: 07/08/2014, 06:22

... |X|≥k. Note that the minpaths and mincuts of (E,φ)are the k-subsets and (n − k + 1)-subsets of E, respectively. Now, let E be totally ordered, and for k-subsets X and Y of E define X  Y :⇔ x ≤ ... network and φ(X) = 1 if and only if X contains the edges of an s, t-path. For source-to-T -terminal reliability we take Σ = (E,φ), where E is the edge-set of the network and φ(X)=1 if...

Ngày tải lên: 07/08/2014, 06:22

... transposing theentries 0and1 atindices 1and2 of(µ + α)[ ] or by transposing the entries −2 and −3 at indices 3 and 4. The result can be written as (4, 3, 3, 2, 2)[ ] respectively as (4, 2, 4, 1, 3)[ ], and indeed ... Corollary. For λ, µ ∈Pand α ∈C, the Kostka number K λ/µ,α equals the number # SST(λ/µ, α) of semistandard tableaux of shape λ/µ and weight α ,and K  λ/µ,α is the number...

Ngày tải lên: 07/08/2014, 08:22

... within the circle and do not cross each other. Noncrossing trees have been studied by Deutsch, Feretic and Noy [2], Deutsch and Noy [3], Flajolet and Noy [4], Noy [6], Panholzer and Prodinger [7]. ... ··· ,C r and C  1 ,C  2 , ··· ,C  r are the cycles encountered in the edge deletion procedures for T and T  .Since(i 1 ,i 2 ) /∈ E(T ), we may assume that (i 1 ,i 2 ) ∈ E(C j )...

Ngày tải lên: 07/08/2014, 13:21

... ∪ . VB(K) and the edges are partitioned E(K) = EW(K) ∪ . EG(K) ∪ . EB(K). The sets VW and VB are the white and black vertices, respectively, and the sets EW, EG and EB are the white, gray and black ... of graphs. The theorems of Erd˝os and Stone [15] and Erd˝os and Simonovits [14] give that d ∗ (M) = 1/r, where r = min{χ(F ) − 1 : F ∈ M} and p ∗ (M) = 1. Alon and Stav,...

Ngày tải lên: 07/08/2014, 15:23

... λ v 1 := 1 and λ v 2 := a, (7) and this partial coloring is extendable, at first to v 5 , with λ v 5 = 3 , then to x 1 , x 2 and to v 6 , and finally to v 3 , which still has the two colors b = a and ... in V P (42) with respect to ℓ + η and G . If u 0 /∈ V ′ C then, on one hand, w has no neighbor in V ′ C , and V ′ C ∪ {w} is independent in G , on the other hand, as we have see...

Ngày tải lên: 07/08/2014, 21:21

... Examples 5.1 and 5.2).  6 Counting Trees and Forests Let us now extend Propositions 5.2 and 5.3 from paths to trees and forests. In Sec- tion 6.1 we consider classes T m (X) of trees and F m (X, ... maxmaxflow and put it in the context of some other well-known g r aph invariants (notably maximum degree and its relatives and degeneracy number). In Section 3 we analyze cocycle b...

Ngày tải lên: 08/08/2014, 12:22