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A Statistical Study of the Kostka-Foulkes Polynomials

โœ Scribed by G.N. Han

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
492 KB
Volume
14
Category
Article
ISSN
0196-8858

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โœฆ Synopsis

The sum of the series (\sum_{n \geq 0} 0^{n} K_{\lambda} \cup a^{n} \cdot \mu \cup a^{n}(q)), where (K_{\nu, \theta}(q)) denotes the Kostka-Foulkes polynomial associated with tableaux of shape (\nu) and evaluation (\theta), is explicitly derived in the case (a=1, q=1) and (\mu=11 \cdots 1). This sum is a rational function (P_{\lambda}(1-z) /(1-z)^{|\lambda|+1}), where the numerator is the generating polynomial for the tableaux of shape (\lambda) by their first letter "pre." Another statistic "deu" is defined on the Young tableaux and the distribution of the pair (pre, deu) is symmetric over the set of the tableaux of the same shape. Finally an explicit calculation is made for the sum of the series (\Sigma_{n \geq 1} K_{t 1^{n}}(q) z^{n}) (arbitrary (q) ) for the tableaux that are extensions (t 1^{n}) of a given tableau (t). 1993 Academic Press, Inc.

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