Báo cáo toán học: " Enumeration of Tilings of Diamonds and Hexagons with Defects" potx

... Aztec diamond of order 3. We are interested in tilings of hexagons with lozenges, which are rhombi with unit sides and angles of 120 and 60 degrees, and tilings of Aztec diamonds with dominoes, which ... number of tilings of half of a hexagon or half of a diamond, with dents at given places. This is not new: see [7] and [8]. 2. Express the number of...

Ngày tải lên: 07/08/2014, 06:20

... cells, and dihedral if every tile of τ is congruent to one of two fixed sets X and Y (prototiles of τ). We shall denote by Ω(X, Y ) the set, up to isomorphism, of all dihedral f -tilings of S 2 whose ... spherical triangle of angle α  α > π 3  and side a and T 2 a scalene spherical triangle of angles δ, γ, β, with the order relation δ < γ < β (β + γ + δ >...

Ngày tải lên: 07/08/2014, 21:20

... Combinatorial Structure of the Dihedral f -Tilings of the Sphere by Equilateral and Scalene Triangles with adjacency of type III In Table 2 is shown a complete list of all spherical dihedral f -tilings, whose ... dihedral f -tilings with adjacency of type III. As we shall see in this case we will find two families of tilings, E α and G k , with the same particularity,...

Ngày tải lên: 07/08/2014, 21:21

... 275−284. [8] R. J. Dawson, Tilings of the sphere with isosceles triangles, Disc. and Comp. Geom., 30 (2003), 467−487. [9] R. J. Dawson and B. Doyle, Tilings of the sphere with right triangles I: ... prototiles are P r and T . From now on P r (r ≥ 5) is a r-sided regular polygon of internal angle α and edge length a and T is a spherical triangle of internal angles β,...

Ngày tải lên: 07/08/2014, 15:23

... 6.26 The right hand side of equation 6.26 is counting pairs (P, Q) of standard tableaux of respective weights k and n. If we add a row of length n − k to the left tableau P and fill it with the numbers ... number of pairs of standard tableaux (P, Q) of same shape where the first row of the tableau P is filled with the numbers 1, 2, . . . , n − k. Corollary 6.2 For every p...

Ngày tải lên: 08/08/2014, 01:20

... of all vertices of T and even splitting of all vertices of V − T. If the edge f  of G s is the image of the edge f of G then we let x s f  = x f . We let x s e =1for the remaining edges e of ... distribution of C is the sequence A 0 ,A 1 , ,A n where A i equals the number of codewords of C of weight i,0≤i≤n. The dual code of C is denoted by C ∗ and consists of...

Ngày tải lên: 07/08/2014, 06:20

... valuation of each factor, and thus of the entire product. Let ζ be a primitive (2n + 1)-st root of unity, and define α i,j = ζ i + ζ −i + ζ j + ζ −j . Then the number of domino tilings of a 2n × ... journal of combinatorics 6 (1999), #R14 As a warm-up in using 2-adic methods, and for the sake of completeness, we will prove that that number of tilings of a 2n × 2n sq...

Ngày tải lên: 07/08/2014, 06:20

... left-hand (resp. right-hand) side of (2). The aim of this paper is to find a combinatorial proof of (2). In Section 2 we construct the sets F bi n of labeled bicolored forests on [n]andD n of certain ... ) n!  v∈α 1 h(v) , which coincides with RHS n . the electronic journal of combinatorics 11(2) (2005), #N3 3 A combinatorial pro of of Postnikov’s identity and a generalized...

Ngày tải lên: 07/08/2014, 08:22

... limit distribu- tions of the number of edges in a random dissection and in a random outerplanar graph, respectively. Proof of Theorem 1.4. The limit distribution of the number of edges in a two-connected unlabeled ... extension of our analysis of properties of random outerplanar graphs to other natural parameters. E.g., while Theorem 5.1 allows to compute the distribution o...

Ngày tải lên: 07/08/2014, 15:23

... Proof of Theorem 7.1. Ignoring the case with only o ne block of odd length, fix a choice of s elements from [a + 1,n] to be placed in the first two blocks. We have shown that more of these ... n, generalising the results with λ = 0 from [9]. In our proofs, we will use the following convent io ns. If λ is a positive integer, and (π,C) is a permutation with a colouring of some...

Ngày tải lên: 07/08/2014, 21:21