Báo cáo toán học: "Mr Paint and Mrs Correct" pot

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

... 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 ... the two trees, and therefore a unique bijection between tournament sequences and Meeussen sequences which respects the ideas of extending or truncating a sequence. To better understand Meeus...

Ngày tải lên: 07/08/2014, 06:20

... 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 and 2, ... 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 remain...

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

... measurements, and drafted the manuscript. CY conducted the STEM measurement. SZ, TH, and GH conducted the MBE growth. JH, WW, and CH coordinated the study. WL provided the idea and conceived ... identified as the indirect transition from the InGaAs conduction band to the GaSb hole level (type-II) and the GaSb QDs direct interband transition (type-I) respectively, as shown in Fi...

Ngày tải lên: 20/06/2014, 20:20