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On Combinatorics of Al-Salam Carlitz Polynomials

✍ Scribed by Dongsu Kim

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 260 KB
Volume: 18
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0094

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✦ Synopsis

A new combinatorial interpretation of the moments of Al-Salam Carlitz polynomials as 'striped' skew-shapes is used to explain the cancellation in the moments of Viennot theory for these polynomials .

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We give a proof, following an argument of Lenstra, of the conjecture of Carlitz (1966) as generalized by Wan (1993). This says that there are no exceptional polynomials of degree \(n\) over \(\mathbb{F}_{q}\) if \((n, q-1)>1\). Fried, Guralnick, and Saxl previously proved Carlitz's conjecture: there