Báo cáo toán học: "Lattice paths, sampling without replacement, and limiting distributions" pps

... electronic journal of combinatorics 16 (2009), #R67 5 Lattice paths, sampling without replacement, and limiting distributions M. Kuba, A. Panholzer and H. Prodinger ∗ Institut f¨ur Diskrete Mathematik ... known sampling without replacement urn. We provide limiting distribution results for the underlying random variable, obtaining a total of five phase changes. Keywords: Lat...

Ngày tải lên: 07/08/2014, 21:21

... the knights to jump over the barriers as long as they start and land inside the band. Special cases: Lattice paths with steps →, ↑, and κ-weighted diagonal steps  (king moves) are obtained from ... with [d] in the rectangle 0 ≤ m<uand 0 ≤ n<W, and has recursive initial values along the whole lower barrier. Let [d −1 ] ≡ [0], and suppose  d k−1  and ˆ d k [m, n]=d k−1 [m, n]...

Ngày tải lên: 07/08/2014, 06:22

... ···I k ={l k−1 +1,l k−1 +2,···,n−1 }and A is a selection of one 132-avoiding permutation on every I 2k ,fork≥1, and one 231-avoiding permutation on every I 2k+1 ,fork≥1, or vice versa, and the selection of ... c n =  2n n  /(n + 1), the nth Catalan number, and that there is a natural bijection between these permutations and lattice paths from (0, 0) to (j, j) using steps (0, 1) an...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 05/08/2014, 15:21

... Mengerian hypergraph if and only if Δ is a Fulkersonian hypergraph and R[It] is normal. In an earlier paper, Escobar, Villarreal and Yoshino showed that I (k) = I k for all k ≥ 1 if and only if Δ is ... North-Holland, Amsterdam, 1989. 2. H. Duc h et, Hypergraphs, Handbook of Combinatorics, Vo l. 1, Elsevier, Amsterdam, 1995, 381–432. 3. C.A. Escobar, R. Villarreal, and Y. Yoshino, T...

Ngày tải lên: 06/08/2014, 05:20

... of a standard tableaux T λ of shape λ and vacillating tableaux P λ of shape λ and length 2k for some λ ∈ Λ k n . Our bijection uses jeu de taquin and RSK column insertion. If T is a standard ... of d ∈ A k in a specific way: connect vertices i and j,withi ≤ j, if and only if i and j are related in d and there does not exist k related to i and j with i<k<j. In this way, ea...

Ngày tải lên: 07/08/2014, 08:22

... which combines efficient sampling, handling of vehicle interaction, and reliable ob- servation modeling. The proposed method is based on the use of Markov chain Monte Carlo (MCMC) approach to sampling (instead ... ) k |z 1:k )  (4) This implies that, if the posterior probability of the candidate sample is larger than that of s (τ ) k the candidate sample is accepted, and if it is smalle...

Ngày tải lên: 20/06/2014, 20:20

... ,r p and s 1 , ,s p correspond- ing to the rows and symbols respectively. When such a graph is made from the entries in columns a and b of M, let the graph be called G andwhenthecolumnsa and b ... ,whileG  comes from columns 1 and b of S  . Note that G  can be obtained from G by deleting the edges r b s 1 and r 2b−1 s b and replacing them with r b s b and r 2b−1 s 1 . Consi...

Ngày tải lên: 07/08/2014, 06:20

... shown that w ∈ Im φ if and only if φ(θ(w)) = w. Example 1: Let n =8,d= 2, and w =1,2,2,1/1,1,2,2. Then A 1 = {1, 4}, and B 1 = {1, 2},soθ(w)(1) = 2 and θ(w)(4) = 1; A 2 = {2, 3} and B 2 = {3, 4},soθ(w)(2) ... M. Gessel and Doron Zeilberger, Random walk in a Weyl chamber, Proc. Amer. Math. Soc. 115 (1992), no. 1, 27–31. [3] David J. Grabiner and Peter Magyar, Random walks in Weyl...

Ngày tải lên: 07/08/2014, 06:22

... get ξ m−1 − δ m ξ m = n m and ξ k − δ k+1 ξ k+1 = n k . (16) We deduce that n m and n k are both non-zero and therefore that ξ m−1 and δ k+1 ξ k+1 are both non-zero integers and sin πξ m−1 =sinπδ k+1 ξ k+1 = ... axis-aligned rectangles in R d with sides of arbitrary length and disjoint interiors. Assume also that Q and R have a vertex K in common and inter- section of odd codi...

Ngày tải lên: 07/08/2014, 06:22