Báo cáo toán học: "Permutation Separations and Complete Bipartite Factorisations of Kn,n" pot

... where p and q are coprime and resolves the BAC Conjecture when p and q are coprime and either p or q is even. For the special case of factorisations of balanced complete bipartite graphs K n,n and ... 8 Permutation Separations and Complete Bipartite Factorisations of K n,n Nigel Martin Department of Mathematics University of Durham, Durham, U.K. nigel.marti...

Ngày tải lên: 07/08/2014, 08:20

... number of permutations of n letters that contain one (132) pattern and have exactly r (123)’s, we write A 2 (r, z):=  n g r (n)z n .ThenA 2 (r, z)isthe coefficient of q r in the series development of ... theorem, and then study some consequences and generalizations. 1 The patterns Let the weight of a permutation π of |π| letters be z |π| q |123(π)| t |12(π)| ,inwhich|123(π)|...

Ngày tải lên: 07/08/2014, 06:20

... consider a weakening of the definitions of uniform and perfect one-factorizations of the complete graph. Basically, we want to order the 2n − 1 one-factors of a one-factorization of the complete graph ... all starters in Z 9 by computer and report that no ordering of the translates of any of these starters yields a sequentially uniform one-factorization of K 10 of t...

Ngày tải lên: 07/08/2014, 08:22

... identities and give bijective proofs of identities involving F I n (x, y, q). These proofs use the same techniques of Benjamin and Quinn [1], and Goyt and Sag an [6]. the electronic journal of combinatorics ... distribution of two different statistics. Let c(σ) be the number of cycles of σ and c i (σ) to be the number of cycles of σ of length i, where the length of...

Ngày tải lên: 08/08/2014, 01:20

... subsequence of the permutation Φ(T ). This completes the proof. Given two labels i and j of T , the following lemma shows that the relative order of i and j in Φ(T ) can be determined by the order of ... dots of P and Q, and then consider the resulting alternating paths P ′ and Q ′ . Let p e (or p ′ e ) denote the last dot of the path P (or P ′ ) and let q e (or q ′ e...

Ngày tải lên: 08/08/2014, 14:23

... Peter L Collins 2 and Siba K Samal* 1 Address: 1 Virginia-Maryland Regional College of Veterinary Medicine, University of Maryland, College Park, Maryland, USA and 2 Laboratory of Infectious ... members of the subfamily Paramyxovirinae with the exception of presence of the SH gene in APMV-6 of Avulavirus, SV5, MuV of Rubulavirus, J virus, BeV, and U gene in FDLV [1,3...

Ngày tải lên: 20/06/2014, 01:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

... contradicts the choice of M and completes the proof of the proposition.  6 Sums of two 2-matroids Let Q 1 and Q 2 be 2-matroids. When Q 1 and Q 2 have the same ground-set and skew classes we shall ... the choice of M and completes the proof of the proposition.  Proposition 5.3 Let P = (U, Ω, R) be a parity system, F be a double flower in P and P  = (U, Ω, R  ) be a...

Ngày tải lên: 07/08/2014, 06:20

... recall three of them and introduce some reformulations of these definitions. For more about the Bruhat order, including details and proofs of the equivalence of Definitions 1, 2, and 3, see [BB], ... j)) satisfy the hypotheses of Lemma 2. First, f u and f w match on columns 1, ,i,sincef σ and f w do. Let N be the number of elements of the set {σ −1 (k) | σ −1 (k) <σ −...

Ngày tải lên: 07/08/2014, 13:21