共查询到20条相似文献,搜索用时 0 毫秒
1.
Rosena R.X. Du 《Journal of Combinatorial Theory, Series A》2010,117(3):345-353
For a labelled tree on the vertex set [n]:={1,2,…,n}, define the direction of each edge ij to be i→j if i<j. The indegree sequence of T can be considered as a partition λ?n−1. The enumeration of trees with a given indegree sequence arises in counting secant planes of curves in projective spaces. Recently Ethan Cotterill conjectured a formula for the number of trees on [n] with indegree sequence corresponding to a partition λ. In this paper we give two proofs of Cotterill's conjecture: one is “semi-combinatorial” based on induction, the other is a bijective proof. 相似文献
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Seunghyun Seo 《Journal of Combinatorial Theory, Series A》2007,114(7):1357-1361
A leader of a tree T on [n] is a vertex which has no smaller descendants in T. Gessel and Seo showed that
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Mingjin Wang 《Journal of Mathematical Analysis and Applications》2010,365(2):653-468
In this paper, we give an extension of the q-beta integral. Applications of the extension are also given, which include to derive an extension of the q-Pfaff-Saalschütz formula, an extension of the Kalnins and Miller transformations and a new identity for . 相似文献
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Victor J.W. Guo Martin Rubey Jiang Zeng 《Journal of Combinatorial Theory, Series A》2006,113(7):1501-1515
Recently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula involving Salié's coefficients for the alternating sums of powers. In this paper, we show that these are polynomials with symmetric, nonnegative integral coefficients by refining Gessel-Viennot's combinatorial interpretations. 相似文献
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Yilmaz Simsek 《Applied mathematics and computation》2010,216(10):2976-973
The main purpose of this paper is to construct a family of modified p-adic twisted functions, which interpolate the modified twisted q-Bernoulli polynomials and the generalized twisted q-Bernoulli numbers at negative integers. We also give some applications and examples related to these functions and numbers. 相似文献
8.
Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah–Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah–Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities. 相似文献
9.
Hjalmar Rosengren 《Journal of Combinatorial Theory, Series A》2008,115(3):376-406
We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series, and as determinants and pfaffians of continuous q-ultraspherical or continuous q-Jacobi polynomials. As special cases, we obtain simple closed formulas for staircase-type partitions. 相似文献
10.
Let be a connected graph with vertex set and edge set . For a subset of , the Steiner distance of is the minimum size of a connected subgraph whose vertex set contains . For an integer with , the Steiner-Wiener index is . In this paper, we introduce some transformations for trees that do not increase their Steiner -Wiener index for . Using these transformations, we get a sharp lower bound on Steiner -Wiener index for trees with given diameter, and obtain the corresponding extremal graph as well. 相似文献
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The paper deals with a sequence of linear positive operators introduced via q-Calculus. We give a generalization in Kantorovich sense of its involving qR-integrals. Both for discrete operators and for integral operators we study the error of approximation for bounded functions and for functions having a polynomial growth. The main tools consist of the K-functional in Peetre sense and different moduli of smoothness. 相似文献
13.
In this paper, the approximation properties of q-Durrmeyer operators Dn,q(f;x) for f∈C[0,1] are discussed. The exact class of continuous functions satisfying approximation process limn→∞Dn,q(f;x)=f(x) is determined. The results of the paper provide an elaboration of the previously-known ones on operators Dn,q. 相似文献
14.
Hao Pan 《Discrete Mathematics》2006,306(17):2118-2127
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers. 相似文献
15.
The definition of the pα-, pβ- and pγ-duals of a sequence space was defined by Et [Internat. J. Math. Math. Sci. 24 (2000) 785-791]. In this paper we compute pα- and N-duals of the sequence spaces Δmv(X) for X=?∞, c and c0, and compute β- and γ-duals of the sequence spaces Δmv(X) for X=?∞, c and c0. 相似文献
16.
Guangjun Zhao 《Discrete Mathematics》2007,307(22):2861-2865
A new q-analogue of the sum of cubes is given with a combinatorial interpretation on the lattice of subspaces. 相似文献
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In the previous papers [J. Boos, T. Leiger, Dual pairs of sequence spaces, Int. J. Math. Math. Sci. 28 (2001) 9-23; J. Boos, T. Leiger, Dual pairs of sequence spaces. II, Proc. Estonian Acad. Sci. Phys. Math. 51 (2002) 3-17], the authors defined and investigated dual pairs (E,ES), where E is a sequence space, S is a BK-space on which a sum s is defined in the sense of Ruckle [W.H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, 1981], and ES is the space of all factor sequences from E into S. In generalization of the SAK-property (weak sectional convergence) in the case of the dual pair (E,Eβ), the SK-property was introduced and studied. In this note we consider factor sequence spaces E|S|, where |S| is the linear span of , the closure of the unit ball of S in the FK-space ω of all scalar sequences. An FK-space E such that E|S| includes the f-dual Ef is said to have the SB-property. Our aim is to demonstrate, that in the duality (E,ES), the SB-property plays the same role as the AB-property in the case ES=Eβ. In particular, we show for FK-spaces, in which the subspace of all finitely non-zero sequences is dense, that the SB-property implies the SK-property. Moreover, in the context of the SB-property, a generalization of the well-known factorization theorem due to Garling [D.J.H. Garling, On topological sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967) 997-1019] is given. 相似文献
18.
Vijay Gupta 《Journal of Mathematical Analysis and Applications》2011,377(2):471-480
In the present paper we propose the q analogue of the modified Beta operators. We apply q-derivatives to obtain the central moments of the discrete q-Beta operators. A direct result in terms of modulus of continuity for the q operators is also established. We have also used the properties of q integral to establish the recurrence formula for the moments of q analogue of the modified Beta operators. We also establish an asymptotic formula. In the end we have also present the modification of such q operators so as to have better estimate. 相似文献
19.
Ranks of q-Ary 1-Perfect Codes 总被引:1,自引:1,他引:0
The rank of a q-ary code C of length n, r(C), isthe dimension of the subspace spanned by C. We establish the existence of q-ary 1-perfectcodes of length
for m 4 and r(C)= n – m + s for each s {1,,m}. This is a generalization of the binary case proved by Etzion and Vardy in[4]. 相似文献
20.
The paper aims to investigate the convergence of the q -Bernstein polynomials Bn,q(f;x) attached to rational functions in the case q>1. The problem reduces to that for the partial fractions (x−α)−j, j∈N. The already available results deal with cases, where either the pole α is simple or α≠q−m, m∈N0. Consequently, the present work is focused on the polynomials Bn,q(f;x) for the functions of the form f(x)=(x−q−m)−j with j?2. For such functions, it is proved that the interval of convergence of {Bn,q(f;x)} depends not only on the location, but also on the multiplicity of the pole – a phenomenon which has not been considered previously. 相似文献