Báo cáo toán học: "Noncrossing Trees and Noncrossing Graphs" pot

... the root with 0 and unroot the tree. We obtain a labelled tree T m on n + 1 vertices, andonecaneasilycheckthatthemapm→ T m is a bijection between maximal chains of NC n+1 and labelled trees on n ... Simion and R. Stanley, Flag-symmetry of the poset of shuffles and a local action of the symmetric group, in preparation. [27] R. Simion and D. Ullman, On the structure of the lattice of...

Ngày tải lên: 07/08/2014, 06:22

... n.LetI B and I S be subsets of [k] and let B = {C i : i ∈ I B } and S = {C i : i ∈ I S }. We refer to the sets B and S as the bases and summits of G respectively. A set C i ∈BiscalledabaseofG and ... line, and then we connect n to the lefthand endpoint of the first cycle, the righthand endpoint of each cycle to the lefthand endpoint of the cycle following it, and we connect the...

Ngày tải lên: 07/08/2014, 06:23

... and geometry. II, 537–615, Springer, Berlin, 2007. [2] Connes, A. and Kreimer, D., Hopf algebras, renormalization, and noncommutative geometry. Comm. Math. Phys. 199 203-242 (1998). [3] Gelfand ... P C (T ) and a colored rooted tree R C (T ), where the latter is the component containing the root. The empty and full cuts C null , C full , where (P C null (T ), R C null (T )) = (∅, T...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 10:20

... 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

... (1995), 313–316. [12] West, J. Generating trees and the Catalan and Schr¨oder numbers. Discrete Math. 146 (1995), 247–262. [13] West, J. Generating trees and forbidden subsequences. Proceedings ... bijection between the two trees, and therefore a unique bijection between tournament sequences and Meeussen sequences which respects the ideas of extending or truncating a sequence....

Ngày tải lên: 07/08/2014, 06:20

... 4 2 Lattice paths and ordered trees We draw our ordered trees with the root at the top and proceed downward to the leaves. The first leaf is the leftmost leaf in the drawing and the remaining ... pattern and that T is among the smallest such trees. We let v 3 be a vertex in T that provides the 3 in such a pattern and let v 1 ,v 2 be the vertices that provide the corresponding 1...

Ngày tải lên: 07/08/2014, 06:20

... |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

... ∪ . 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