Polynomials with palindromic and unimodal coefficients |
| |
Authors: | Hua Sun Yi Wang Hai Xia Zhang |
| |
Institution: | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China |
| |
Abstract: | Let f(q)=arqr+···+ asqs, with ar=0 and as=0, be a real polynomial. It is a palindromic polynomial of darga n if r+s=n and ar+i=as-i for all i. Polynomials of darga n form a linear subspace Pn(q) of R(q)n+1 of dimension n/2]+1. We give transition matrices between two bases {qj(1+q+··· +qn-2j)},{qj(1+q)n-2j and the standard basis qj(1+qn-2j) of Pn(q). We present some characterizations and sufficient conditions for palindromic polynomials that can be expressed in terms of these two bases with nonnegative coefficients. We also point out the link between such polynomials and rank-generating functions of posets. |
| |
Keywords: | Unimodal sequence palindromic sequence linear space poset |
本文献已被 CNKI SpringerLink 等数据库收录! |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学学报(英文版)》下载免费的PDF全文 |