Name
Title | ||
|---|---|---|
Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials |
Abstract | ||
|---|---|---|
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of separation of variables. We illustrate our approach by applying it to determine the number of perfect matchings, derangements, and other weighted permutation problems. The separation of variables technique naturally leads to integral representations of combinatorial numbers where the integrand contains a product of one or more types of orthogonal polynomials. This also establishes the positivity of such integrals. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jcta.2012.10.007 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
combinatorial number,orthogonal polynomial,weighted permutation problem,perfect matchings,integral representation,linearization coefficient problem,new approach,combinatorial interpretation,difference system,variables technique,separation of variables,derangements,orthogonal polynomials | Discrete mathematics,Wilson polynomials,Combinatorics,Classical orthogonal polynomials,Orthogonal polynomials,Gegenbauer polynomials,Discrete orthogonal polynomials,Jacobi polynomials,Hahn polynomials,Mathematics,Kravchuk polynomials | Journal |
Volume | Issue | ISSN |
120 | 3 | 0097-3165 |
Citations | PageRank | References |
2 | 0.47 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mourad E. H. Ismail | 1 | 75 | 25.95 |
| Anisse Kasraoui | 2 | 60 | 7.41 |
| Jiang Zeng | 3 | 145 | 24.69 |