Báo cáo toán học: "Chromatic statistics for triangulations and Fuß–Catalan complexes" ppsx

... (Theorems 1.1, 1.2, 2.1, and 2.2) present refinements of the plain enumeration of triangulations and Fuß–Catalan complexes arising from certain vertex-colourings of triangulations and Fuß–Catalan complexes, ... , by introducing colour statistics for triangulations and Fuß–Catalan complexes. Our refinements consist in showing that the number of triangulations, respective...

Ngày tải lên: 08/08/2014, 14:23

... by the appropriate formulas from the right side of (24). Specifically, write A  for A(N, m,v 0 , ,v m−1 ), write P  j for P j (N,m, v 0 , ,v m−1 ), and so forth. Write A  for A(N − v 0 ,m,v 1 , ... t)=C n (t, q) for all n, since this symmetry property holds for RC n . (It is also easily deduced from the formula for OC n , by replacing the summation index µ by the conjugate of...

Ngày tải lên: 07/08/2014, 08:22

... log d  and assume k ≥ 3. We randomly g enerate a graph G with vertex set [2k] d . As before an element z in [d] ×[2k] d−1 designates a line in [2k] d parallel to some axis. We place a random perfect ... d ≥ 2. The integers k and d are fixed, and N is a large integer to be chosen in terms of k and d. Consider the set [N] d . For each v ∈ [N] d , define a random d-tuple X(v) such tha t...

Ngày tải lên: 07/08/2014, 21:21

... q 2 ) ∞ . Here and in the sequel, we will use the following standard q-series notation: (a; q) ∞ := ∞  n=1 (1 − aq n−1 ), | q| < 1. Since a partition congruence for a(n) is deduced from the equation for ... x 5 (mod 5) for the first equiva lence and applied the Jacobi’s identity [2, Theorem 1.3.9] for the final equivalence. the electronic journal of combinatorics 18 (2011), #P12...

Ngày tải lên: 08/08/2014, 14:23

... harmonic functions. We give also a Guelfond and Polya type theorem in the case of harmonic function. 2. Notations and Results For all z = re iθ ∈ C and n ∈ N we put: e 1 (z) ≡ 1,e n (z)=  r k cos ... Ma y 24, 2004 Abstract. For harmonic and separately harmonic functions, we give results similar to the Carlson-Boas theorem. We give also harmonic analogous of the Polya and Guelfo...

Ngày tải lên: 06/08/2014, 05:20

... the expansions for β(A) in terms of convex subsets generally have a simpler form than other expansions. In particular, the forms given for β(A) in Propositions 4.1, 4.2, 4.5, and 4.7 seem especially ... connectivity result for matroids (Theorem 7.3.2 of [28]): β(M)=0ifandonlyifM=M 1 ⊕M 2 (and M is not a loop). The converse of Proposition 2.3 is false for greedoids: It is possible...

Ngày tải lên: 07/08/2014, 06:20

... |Γ|≤m! and the subset {y 1 , ,y j } satisfies 1. φ(y i )=i for each i, 2. y i+1 is in Γ i−1 .y i for each i from 2 to j − 1, and y 1 is in Γ j−1 .y j , then j ≤ m and |Γ i−1 .y i |≥j − i + 2for each ... φ O and φ X\O . Consequently g is in the subgroup Stab(O) ∩ Stab(X\O)andsog is in Stab(X). This gives a numerical condition for 2-distinguishability. Corollary 2.4. Suppose Γ act...

Ngày tải lên: 07/08/2014, 08:20

... V (K N ) and edge set E = E(K N ). For x, y ∈ V , let xy denote the edge between the two vertices x and the electronic journal of combinatorics 15 (2008), #R49 1 Let n ≥ 2 and let E r and E b be ... R α = {(x, y) : c(xy) = α}, and let | stand for ordinary composition of binary relations, ie. R α |R β := {(x, z) : ∃y (x, y) ∈ R α , (y, z) ∈ R β }, then conditions (i) and (ii) i...

Ngày tải lên: 07/08/2014, 15:23

... the Japan Society for the Promotion of Science and the Hungarian Academy of Science, the Hungarian National Foundation for Scientific Research (OTKA T049409), and the Grant-in-Aid for Scientific Research ... are based on the results in [2] and [5]. Lemma 3.1. For any u ∈ X + , there exist unique q ∈ Q and i ≥ 1 such that u = q i . Lemma 3.2. Let i ≥ 1,letu, v ∈ X ∗ and let uv...

Ngày tải lên: 06/08/2014, 05:20

... by Moon and Moser [3]. Furthermore, I(n, n − 2) = 2 n−2 − 2 and the extremal graph (unique up to isomorphism) coincides with K 2,n−2 for every n ≥ 4. In [10] it was proved that for sufficiently ... that x i ∈ c i \  j=i c j for every i =1, ,n− k.DenotingX = {x 1 , ,x n−k } and Y = V (G)\ X one has |Y | = k.Each clique c i consists of x i and a subset of Y . For every subset A...

Ngày tải lên: 07/08/2014, 06:23