Some Combinatorics of the Hypergeometric Series

Jacques Labelle, Yeong Nan Yeh
1988 European journal of combinatorics (Print)  
Symmetry formulas for the classical hypergeometric series 2 FI are proved combinatorially. The idea of the proofs is to find weighted combinatorial structures which form models for each side of the formula and to show how to go from the first to the second model by a 'weak isomorphism' (i.e. a sequence of isomorphisms, regroupings and degroupings of structures). This is then applied to the four 2 FI-families (Meixner. Krawtchouk, Meixner-Pollaczek and Jacobi) of hypergeometric orthogonal
more » ... ials. We give three 'weakly isomorphic' models for each family and prove in a completely combinatorial way the 3-terms recurrences for these polynomials.
doi:10.1016/s0195-6698(88)80056-8 fatcat:eq4ikfom4behlii3symhsprmhy