Báo cáo toán học: " Orthogonal polynomials represented by CW -spheres" pdf

... ,m n−1 )maybe given by (θ 1 , ,θ n−1 ) → (θ 1 , ,θ n−2 ,θ  n−1 ) the electronic journal of combinatorics 11(2) (2004), #R4 16 5 A sequence of orthogonal polynomials represented by lune complexes In ... homeomorphic to a sphere. By [7], P is a CW- poset if and only if it is the face poset P(Ω) of a regular CW- complex Ω. When Ω is a CW- sphere, the poset P 1 (Ω), obtained from...

Ngày tải lên: 07/08/2014, 08:22

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Ngày tải lên: 05/08/2014, 15:20

... = i. A 2 -orthogonal coloring is simply called an orthogonal coloring.Thek -orthogonal chromatic number of G,denotedbyOχ k (G), is the minimum possible number of colors used in a k -orthogonal ... colors in c 2 . The notion of orthogonal colorings is strongly related to the notion of orthogonal Latin squares. The orthogonal chromatic number of G, denoted by Oχ(G), is the minimum...

Ngày tải lên: 07/08/2014, 06:20

... alternating permutations as defined by Ehrenborg and Readdy [8]. In §6 we consider the Euler polynomials E n (x), defined by (2) 2e tx e t +1 = ∞  n=0 E n (x) t n n! . Euler polynomials appear in many ... explicit formulas for the values of the Euler polynomials at rational numbers in terms of the P n and Q n . The Euler polynomials E n (x) are defined by equation (2) above; the E...

Ngày tải lên: 07/08/2014, 06:20

... combinatorics 7 (2000), #R40 9 where, for P ∈ A  2 (n), G(P ) is obtained by replacing each blue HV pair by D step and by removing the color from any red turns. Finally, with the maps h : A 0 5 (n) ... Narayana polynomials. The known results of the first two sections serve as background for the results of the last two sections. This paper will consider six step sets which are labeled a...

Ngày tải lên: 07/08/2014, 06:20

... given by u 2 0 = v 2 0 −v 2 0 + π 2 /4 − 2Li(e −v 0 )+ 1 2 Li(e −2v 0 ) . The possibility of evaluating a dilogarithm by asymptotic partition counting was suggested by Andrews and carried out by ... k), the most likely number of parts was computed by Szekeres in [20]. The average number of parts was computed by Luthra in 1957 and was recomputed by Kessler and Livingston in 1976...

Ngày tải lên: 07/08/2014, 06:22

... construct σ i ,i=1, ,nin S n as in Lemma 2.2, by inserting n in position i. Since |n − 1, we have by Lemma 2.4 that for all i, maj(σ −1 ) ≡ maj(σ −1 i )(mod). By Lemma 2.2, since the set {maj(σ i ):i ... σ i ,i=1, ,nin S n as in Lemma 2.2, by inserting n in position i. Since |n − 1, we have by Lemma 2.4 that for all i, maj(σ −1 ) ≡ maj(σ −1 i )(mod). Now let k|n − 1. By Lemma...

Ngày tải lên: 07/08/2014, 06:23

... sequences obtained by deletion of the s 1 -th term from k (1) and l (1) , and similarly ˜ k (2) and ˜ l (2) . By Lemma 3.4, β n−1 (k (1) ,l (1) )=β n−1 (k (2) ,l (2) ), and by the induction hypothesis, ˜ k (1) = ˜ k (2) , ˜ l (1) = ˜ l (2) . The ... thus l  u = l u >l s =(n−1 −r)+p r −s, which is impossible by the definition of the set U. 2. Uniqueness. Again, use induction by n,...

Ngày tải lên: 07/08/2014, 07:21

... (66) where the numbers H n and ϕ n are given by Proposition 3.10. The same method can be applied to weighted C B -graphs where the weight is defined by (11), that is, with the variables (y 2 ,y 3 , ... for Husimi graphs. By summing over the polygon-size distribution, we finally obtain: Proposition 3.6 The number Ca n = | Ca[n]| of (labelled) cacti on [n],forn ≥ 2, is given by Ca n =  k...

Ngày tải lên: 07/08/2014, 08:20

... real. Equivalently, by equation (1), that all roots of its f-polynomial are real. It was recently shown by Br¨and´en [10] that an extension of Neggers conjecture proposed by Stanley is false. ... 12 (2005), #N4 4 Proof. By Birkhoff’s representation theorem (see [18, Ch. 3]) we have that L = J(P ), where J(P ) is the family of order ideals of some poset P ordered by inclusion. Let B d...

Ngày tải lên: 07/08/2014, 08:22