Polynomials with palindromic and unimodal coefficients
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| 024 | 7 | 0 | |a 10.1007/s10114-015-4331-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4331-4 | ||
| 245 | 0 | 0 | |a Polynomials with palindromic and unimodal coefficients |h [Elektronische Daten] |c [Hua Sun, Yi Wang, Hai Zhang] |
| 520 | 3 | |a 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. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Unimodal sequence |2 nationallicence | |
| 690 | 7 | |a palindromic sequence |2 nationallicence | |
| 690 | 7 | |a linear space |2 nationallicence | |
| 690 | 7 | |a poset |2 nationallicence | |
| 700 | 1 | |a Sun |D Hua |u School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China |4 aut | |
| 700 | 1 | |a Wang |D Yi |u School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China |4 aut | |
| 700 | 1 | |a Zhang |D Hai |u School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/4(2015-04-01), 565-575 |x 1439-8516 |q 31:4<565 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4331-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4331-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Sun |D Hua |u School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wang |D Yi |u School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhang |D Hai |u School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/4(2015-04-01), 565-575 |x 1439-8516 |q 31:4<565 |1 2015 |2 31 |o 10114 | ||