Context-free grammars for triangular arrays
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| 024 | 7 | 0 | |a 10.1007/s10114-015-4209-5 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4209-5 | ||
| 245 | 0 | 0 | |a Context-free grammars for triangular arrays |h [Elektronische Daten] |c [Robert Hao, Larry Wang, Harold Yang] |
| 520 | 3 | |a We consider context-free grammars of the form $G = \{ f \to f^{b_1 + b_2 + 1} g^{a_1 + a_2 } ,g \to f^{b_1 } g^{a_1 + 1} \} $ , where a i and b i are integers subject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let T n (x) = Σ k=0 n T(n, k)x k . Based on the differential operator with respect to G, we define a sequence of linear operators P n such that T n+1(x) = P n (T n (x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Brändén, we obtain a necessary and sufficient condition for the operator P n to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh. Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers. | |
| 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 Context-free grammar |2 nationallicence | |
| 690 | 7 | |a stable polynomials |2 nationallicence | |
| 690 | 7 | |a real-rootedness |2 nationallicence | |
| 690 | 7 | |a Bessel numbers |2 nationallicence | |
| 690 | 7 | |a Whitney numbers |2 nationallicence | |
| 700 | 1 | |a Hao |D Robert |u Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, P. R. China |4 aut | |
| 700 | 1 | |a Wang |D Larry |u Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, P. R. China |4 aut | |
| 700 | 1 | |a Yang |D Harold |u Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, 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 31/3(2015-03-01), 445-455 |x 1439-8516 |q 31:3<445 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4209-5 |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/s10114-015-4209-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hao |D Robert |u Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wang |D Larry |u Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Yang |D Harold |u Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, 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 31/3(2015-03-01), 445-455 |x 1439-8516 |q 31:3<445 |1 2015 |2 31 |o 10114 | ||