Herbert S. Wilf
Published 2004-06-30, updated 2004-09-22Version 2
We apply the method of characteristics for the solution of pde's to two combinatorial problems. The first is finding an explicit form for a distribution that arises in bio-informatics. The second is a question raised by Graham, Knuth and Patashnik abiout a sequence of generalized binomial coefficients. We find an exact formula, which factors in an interesting way, in the case where one of the six parameters of the problem vanishes. We also show that the associated polynomial sequence has real zeros only, provided that one parameter vanishes, and the other five are nonnegative.
$q$-Eulerian polynomials and polynomials with only real zeros
A unified approach to polynomial sequences with only real zeros
Hypergraph Fuss-Catalan Numbers
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