Simion猜想和对数凹性  

Log-Concavity and Simion's Conjecture

作　　者：王毅[1] 赵立中[1] 

机构地区：[1]大连理工大学应用数学系,大连116024

出　　处：《数学学报（中文版）》2004年第3期449-454,共6页Acta Mathematica Sinica：Chinese Series

基　　金：辽宁省自然科学基金(2001102084)

摘　　要：以N(m,n;λ，μ）表示在m×n的矩形格的左上角和右下角分别删掉分拆λ和μ的Ferrers图后从左下角到右上角格路的数目。Simion猜想对任意分拆λ，N（l-k,k;λ,φ)关于k是对数凹的，本文证明了，如果序列x0,x1,…，xn为对数凹的，则序列yk=∑i=k^n(a+i b+k)xi亦为对数凹的，并给出其对Simion猜想的应用。本文还证明对所有分拆λ和μ，N（l-k,k;λ，μ）关于k是对数凹的。Denote by N(m, n;λ,μ) the number of lattice paths from the lower left corner to the upper right corner in an m×n grid with the Ferrers diagrams of two partitions λ and μ being removed from the upper left corner and the lower right corner respectively. Simion's conjectured that N(e-k, k;λ,θ) is log-concave in k. Here we show that if the sequence x_0, x_1,..., x_n is log-concave, then the sequence y_k x_i is also log- concave, and present an application of this result to Simion's conjecture. Furthermore, we show that N(e-k, k;λ,μ) is log-concave in k for all partitions λand μ

关 键 词：格路 单峰 对数凹 

分 类 号：O157.1[理学—数学]