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A Combinatorial Proof of a Recursion for the q-Kostka Polynomials

✍ Scribed by Kendra Killpatrick

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
196 KB
Volume
92
Category
Article
ISSN
0097-3165

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✦ Synopsis

The Kostka numbers K * + play an important role in symmetric function theory, representation theory, combinatorics and invariant theory. The q-Kostka polynomials K * + (q) are the q-analogues of the Kostka numbers and generalize and extend the mathematical meaning of the Kostka numbers. Lascoux and Schu tzenberger proved one can attach a non-negative integer statistic called charge to a semistandard tableau of shape * and content + such that the Kostka polynomial K * + (q) is the generating function for charge on those semistandard tableaux. We will give two new descriptions of charge and prove several new properties of this statistic. These new descriptions of charge will be used to give a combinatorial proof of a content reducing recursion for the q-Kostka polynomials originally proved by

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