Polynomials À La Lehmers and Wilf

20 09 Polynomials Á La Lehmers and Wilf

A Heterosexual Mehler Formula for the Straight Hermite Polynomials (À La Foata)

In my invited talk ‘The unreasonable effectiveness of Combinatorics in Orthogonal Polynomials I’, (July 1, 1998, 10:30-11:30 local time), at the IWOP ’98, Léganes, Madrid, (organized by Paco Marcellan and Renato Alvarez-Nodarse), I described, for most of the hour, Dominique Foata’s[F1] gorgeous and seminal proof of Mehler’s formula. As I got carried away in the exposition, I replaced the origin...

On the Rearrangement Conjecture for Generalized Factor Order Over P

The Rearrangement Conjecture states that if two words over P are Wilf-equivalent in the factor order on P∗ then they are rearrangements of each other. We introduce the notion of strong Wilf-equivalence and prove that if two words over P are strongly Wilf-equivalent then they are rearrangements of each other. We further conjecture that Wilf-equivalence implies strong Wilf-equivalence. Résumé. La...

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Discriminants of Chebyshev-like Polynomials and Their Generating Functions

In his paper of 2000, Kenneth B. Stolarsky made various observations and conjectures about discriminants and generating functions of certain types of Chebyshev-like polynomials. We prove several of these conjectures. One of our proofs involves Wilf-Zeilberger pairs and a contiguous relation for hypergeometric series.