Báo cáo toán học: "Parking Functions and Noncrossing Partitions" pot

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 10:20

... θ 2 B G (r)/2+o u (θ 3 g(r) 1+ ) (19) for all >0. Proof: Using the asymptotic formula for the coefficients of admissible functions and an argument like that in Hayman’s proof of Theorem H.II, the results for a and B follow ... .WeextendR and Θ to include these variables by forming the Cartesian product of R with copies of (0, ∞) and the Cartesian product of Θ...

Ngày tải lên: 07/08/2014, 06:20

... systems on fifteen elements, Mem. Nat. Acad. Sc. USA 14, second memoir (1919) 1-89. Codes, Lattices, and Steiner Systems Patrick Sol´e ∗ , CNRS, I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia ... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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 Meeussen sequences, ... Wouter Meeussen [private communication, 1999], and we here name sequences with this property Meeussen sequences in his honor. Part of their definition is similar to that of...

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 ... 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 rema...

Ngày tải lên: 07/08/2014, 06:20

... Proposition 4.1. GENERATING FUNCTIONS AND GENERALIZED DEDEKIND SUMS Ira M. Gessel Department of Mathematics Brandeis University Waltham, MA 02254-9110 gessel@math.brandeis.edu Submitted: August ... N j (x)andD j (x) are algebraic functions of x,andT(x)isarational function of x.MorepreciselyT(x)is0ifthedegreeofPis less than that of Q, T (x)is−1 if the degree of P is greater, and i...

Ngày tải lên: 07/08/2014, 06:22

... contains both b and d,thenB= B  . We establish some connections between parking functions and noncrossing partitions. A generating function for the flag f -vector of the lattice NC n+1 of noncrossing ... 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 la...

Ngày tải lên: 07/08/2014, 06:22

... to network reliability We consider both directed and undirected networks in which nodes are perfectly re- liable and edges fail randomly and independently with known probabilities. For such networks, ... the 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...

Ngày tải lên: 07/08/2014, 06:22

... motivations of Odlyzko and Wilf, when they study the width of labeled trees, is to give a tight estimate for the average bandwidth of this class of tree. 2 The breadth first search random walk From ... initially (0). Then, at each of the n following stages of the BFS, the vertex x at the head of the queue is removed from the queue, and all “new” neighbor...

Ngày tải lên: 07/08/2014, 06:22

... is a natural action of S n on the set of parking functions, which permutes the a j . There is also an action of S n on the set of factorizations, which goes as follows. We define an action of ... local action of S n on V NC n+1 in [S], Proposition 4.1. Thus we have two actions of S n , one on factorizations and one on parking functions, and the map we are looking at is...

Ngày tải lên: 07/08/2014, 06:23

... from the end of the left list into the stack, and when we encounter an element of p, we move the top of the stack to the beginning of the right list. If an element of p is equal to an element of ... p, p k . At this point, the top of the stack is the index of the last element of q encountered. We move the top of the stack out, as the first entr...

Ngày tải lên: 07/08/2014, 07:21

... (2006), #A5 14 1.4 Alternating polynomials and Schur functions 1.4. Alternating polynomials and Schur functions. Now fix n ∈ N,andletA [n] denote the additive subgroup of Z[X [n] ] of alternating poly- nomials, ... ∈Pand α ∈C, the Kostka number K λ/µ,α equals the number # SST(/à, ) of semistandard tableaux of shape /à and weight ,and K /à, is the number of transposed semista...

Ngày tải lên: 07/08/2014, 08:22

... 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, in [2], prove that d ∗ (Forb(K 1,3 )) ... ∪ . 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 an...

Ngày tải lên: 07/08/2014, 15:23

... uses real paint and varnishes the vertices with it, and that Mrs. Correct uses sandpaper pieces to roughen the paint surface. In this way we o bta in up to ℓ v := |S v | + 1 layers of paint on ... , and le t η u := |N(u) ∩ W | be the number of neighbors of u ∈ U in W . If G[U] is ℓ U -paintable and G[W ] is ℓ W -paintable then G is (ℓ U + ℓ W + η)-paintable; where η := (η u )...

Ngày tải lên: 07/08/2014, 21:21