广义中心三项式系数对数凸性研究
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摘要
构造广义中心三项式三角矩阵,该矩阵为Aigner-Catalan-Riordan矩阵的特例。证明了广义中心三项式系数是广义中心三项式三角矩阵的第0列元素,并以此结果为基础研究了其对数凸性。作为应用,可以统一的证明中心二项式系数、中心Delannoy数各自都构成对数凸序列。
In this paper,we construct generalized central trinominal triangles,which is the special case of Aigner- Catalan- Riordan arrays. We investigate the log- convexity of generalized central trinominal coefficients by proofing the fact that generalized central trinominal coefficients coincide with the first column of the generalized central trinominal triangles. As application,we give the log- convexity of central binominal coefficients and central Delannoy numbers in a unified approach.
In this paper,we construct generalized central trinominal triangles,which is the special case of Aigner- Catalan- Riordan arrays. We investigate the log- convexity of generalized central trinominal coefficients by proofing the fact that generalized central trinominal coefficients coincide with the first column of the generalized central trinominal triangles. As application,we give the log- convexity of central binominal coefficients and central Delannoy numbers in a unified approach.
引文
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[4]NOE T D.On the divisibility of generalized central trinomial coefficients[J].J.Integer Seq.,2006,9(2):Article 06.2.7,12.
[5]WANG Y,ZHANG Z H.Log-convexity of AignerCatalan-Riordan numbers[J].Linear Algebra Appl.,2014,463:45-55.
[6]ZHU B X.Log-convexity and strong q-log-convexity for some triangular arrays[J].Adv.in Appl.Math.,2013,50(4):595-606.
[7]SUN Z H.Congruences concerning Legendre polynomials[J].Proc.Amer.Math.Soc.,2011,139(6):1915-1929.
[8]CAUGHMAN J S,HAITHCOCK C R,VEERMAN J J P.A note on lattice chains and Delannoy numbers[J].Discrete Math.,2008,308(12):2623-2628.
[2]SUN Z W.Congruences involving generalized central trinomial coefficients[J].Sci.China Math.,2014,57(7):1375-1400.
[3]WILF H S.Generatingfunctionology[M].Boston MA:Academic Press,Inc.,1990.
[4]NOE T D.On the divisibility of generalized central trinomial coefficients[J].J.Integer Seq.,2006,9(2):Article 06.2.7,12.
[5]WANG Y,ZHANG Z H.Log-convexity of AignerCatalan-Riordan numbers[J].Linear Algebra Appl.,2014,463:45-55.
[6]ZHU B X.Log-convexity and strong q-log-convexity for some triangular arrays[J].Adv.in Appl.Math.,2013,50(4):595-606.
[7]SUN Z H.Congruences concerning Legendre polynomials[J].Proc.Amer.Math.Soc.,2011,139(6):1915-1929.
[8]CAUGHMAN J S,HAITHCOCK C R,VEERMAN J J P.A note on lattice chains and Delannoy numbers[J].Discrete Math.,2008,308(12):2623-2628.