caa a22 4500 605461783 CHVBK 20210128100245.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10114-015-4331-4 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4331-4 Polynomials with palindromic and unimodal coefficients [Elektronische Daten] [Hua Sun, Yi Wang, Hai Zhang] Let f(q) = a r q r + ⋯ + a s q s , with a r ≠ 0 and a s ≠ 0, be a real polynomial. It is a palindromic polynomial of darga n if r + s = n and a r+i = a s−i for all i. Polynomials of darga n form a linear subspace $$\mathcal{P}_n (q)$$ of ℝ(q) n+1 of dimension $$\left\lfloor {\tfrac{n} {2}} \right\rfloor + 1$$ . We give transition matrices between two bases {q j (1 + q + ⋯ + q n−2j)}, {q j (1 + q) n−2j } and the standard basis {q j (1 + q n−2j)} of P n (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. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Unimodal sequence nationallicence palindromic sequence nationallicence linear space nationallicence poset nationallicence Sun Hua School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China aut Wang Yi School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China aut Zhang Hai School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 565-575 1439-8516 31:4<565 2015 31 10114 https://doi.org/10.1007/s10114-015-4331-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4331-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sun Hua School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China aut NATIONALLICENCE 700 1- Wang Yi School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China aut NATIONALLICENCE 700 1- Zhang Hai School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 565-575 1439-8516 31:4<565 2015 31 10114