Báo cáo toán học: "Bijective counting of tree-rooted maps and shuffles of parenthesis systems" pot

... isomorphic to the construction of Cori et al. via the encoding of tree-rooted maps by shuffles of parenthesis systems. Tree-rooted maps, or alternatively shuffles of parenthesis systems, are in one-to-one correspondence ... between tree-rooted maps of size n and pairs consisting of a tree and a non-crossing partition of size n and n+1 respectively. This simp...

Ngày tải lên: 07/08/2014, 15:22

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:20

... Sons, Inc., 1992. [3] L´aszl´o Babai and Shlomo Moran. Arthur-merlin games: a randomized proof system, and a hierarchy of complexity classes. Journal of Computer and System Sciences, 36(2):254–276, ... is d-distinguishable. Proof. We study the behavior of a random d-coloring of G, the probability distribu- tion given by selecting the color of each vertex independently and un...

Ngày tải lên: 07/08/2014, 06:22

... Statistical Me- chanics of Domains and of Rubber–like Molecules. Phys. Rev. 103, 1-16. [29] T. Vrbov´a and S.G. Whittington, 1996, Adsorption and Collapse of Self-Avoiding Walks and Polygons in Three ... 349) 256n 2       < M n 3 . (59) Proof. The proof of the above is similar to that of Lemma 7. the electronic journal of combinatorics 9 (2002), #R20 21 [6] R. Bra...

Ngày tải lên: 07/08/2014, 06:23

... consisting of the linear polynomial t − 1 and a number of factors of the form t s ±1 such that gcd(m, s) =1. Another of the main results of this paper is a proof of Conjecture 2; see Theorem 3.4 below. 1.2 ... proof of Lemma 5.7. The existence of elements y 2k− i and z i blocking each other is a consequence of the fact that the “y-path” and the “z-path” intersect. Lem...

Ngày tải lên: 07/08/2014, 13:21

... rest of the users, and at the same time maximizes the desired signal power. The ability of fulfilling these requirements depends on the number of DoFs N eff,T and N eff,u , available on the BS and ... the path connecting the jth angle of departure and ith angle of arrival. The amplitude of this component is naturally affected by the complex gains of the transmit and rece...

Ngày tải lên: 20/06/2014, 20:20

... r.The components of λ are called the parts of λ. The integer n, the sum of all the parts of λ, is called the norm of λ and is denoted by n(λ). The (ordinary) Ferrers diagram of λ is an array of cells ... ‘ρ is a cell of λ’. The hook of a cell ρ of the ordinary Ferrers diagram of λ is the set of cells that are either in the same row as ρ and to the right of ρ, or...

Ngày tải lên: 07/08/2014, 06:20

... tree of M. Cut e 0 and e 1 , delete the end of e 0 and start of e 1 and close with a root edge the start of e 0 with the end of e 1 . The map which is obtained is an the electronic journal of combinatorics ... of Eulerian maps can be bicolored and, via the medial graph correspondence, these two colors of faces correspond to vertices and faces of planar maps. Henc...

Ngày tải lên: 07/08/2014, 06:20

... number of permutations σ ∈ S n with maj(σ) ≡ i (mod k)andmaj(σ −1 ) ≡ j (mod ). We give a combinatorial proof of: Theorem 3.1 Let  be a divisor of n − 1,=1, and let k be a divisor of n, k ... electronic journal of combinatorics 9 (2002), #R21 10 On counting permutations by pairs of congruence classes of major index H ´ el ` ene Barcelo and Robert Maule Sheila Sundaram...

Ngày tải lên: 07/08/2014, 06:23