Báo cáo toán học: "Random Sampling of Labeled Tournaments" docx

... result of Kannan, Tetali and Vempala to com- pletely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path ... vector of a tournament is the sequence of out- degrees of the vertices of the tournament. In general, given a score vector with n scores, there can be an exponential (in n) nu...

Ngày tải lên: 07/08/2014, 06:20

... 1. ProofofTheorem3: Let a(G) be the number of automorphisms of an unlabeled n-vertex graph G. The number of distinct labelings of G is n!/a(G). If f (·)isa statistic on graphs, its expectation on labeled ... This finishes the proofofTheorem1. 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 0 0.2 0.4 0.6 0.8 1 t Figure 2: The plot of µ  (t) for 0 ≤ t ≤ 1. 4 Proof of Theorems 2 and 3 Proof o...

Ngày tải lên: 07/08/2014, 07:21

... urn with non-integer numbers of balls. From the case m = 4 we obtain a proof of a conjecture of Warrington. Our result is consistent with a conjectural limiting law of the subnetwork as n → ∞ implied ... urn Funded in part by Microsoft Research and NSERC. the electronic journal of combinatorics 17 (2010), #N23 1 2 Proof of main result We will use the following key properties of...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 09:46

... member of the second coordinate of the label of y, delete the edge x j y.If the digit of z is 3 and y is not a member of the second coordinate of the label of z, delete the electronic journal of ... Subclaims, the proof of our lemma is complete. 5 Proof of the Main Theorem In this section, we present the proof of the main theorem. Let C be a topologically closed class o...

Ngày tải lên: 07/08/2014, 06:23

... spectrum of D a,b,0 (with δ  3). Lemma 3.4. The spectrum of D a,b,0 with δ = gcd(a, b)  3 consists of the eigenvalues of C δ (except 2 and −2) with multiplicity 3, the eigenvalues of C a and ... eigenvalues of C a ∪ C b and be of multiplicity 1. This ends the proof. From the above lemma we know to some extent the spectrum of D a,b,0 . If H is a tentative cospectral mate of...

Ngày tải lên: 08/08/2014, 12:22

... d). Thus the set of characteristic points of the system forms an antichain under the partial ordering ≤. Proof. For the proof assume, in view of Remark 8, that all second partials of the G i with respect ... .} of n onnegative integers, the set Q of rational numbers, the set R of real numbers, and the set C of complex numbers. For the linearly ordered set R of real numbers o...

Ngày tải lên: 08/08/2014, 12:22

... valuation of sequences counting Alternating Sign Matrices. Journal of In teger Sequences, 12:1–21, 2009. [5] D. Zeilberger. Proof of the Alternating Sign Matrix conjecture. Electronic Journal of Combinatorics, ... a careful reading of the manuscript. The work of the second author was partially f unded by NSF-DMS 0713836. References [1] D. Bressoud. Proofs and Confirmations: the sto...

Ngày tải lên: 08/08/2014, 14:23

... sequence of L(F ), the low graph of the underlying multigraph of F . Each vertex- copy is paired to a copy of a vertex of degree k with probability kd k /2n = α. Therefore a.s. a vertex of degree ... more work. We will present this proof in the final section of the paper. The crux of the proof of Theorem 1.2 lies in showing that  k is a threshold for G k n,M in the sense o...

Ngày tải lên: 07/08/2014, 06:20

... electronic journal of combinatorics 11 (2004), #R62 3 Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theorem ZEPH LANDAU Department of Mathematics City College of New York landau@sci.ccny.cuny.edu A LEXANDER ... elements of graph theory, representation theory, and probability theory required for the statement of the theorem and the subsequent proof. The ex...

Ngày tải lên: 07/08/2014, 08:20