Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
نویسندگان
چکیده
منابع مشابه
Explicit formulae for Kerov polynomials
We prove two formulae expressing the Kerov polynomial Σk as a weighted sum over the set of noncrossing partitions of the set {1, . . . , k + 1}. We also give a combinatorial description of a family of symmetric functions specializing in the coefficients of Σk .
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Kerov’s polynomials give irreducible character values of the symmetric group in term of the free cumulants of the associated Young diagram. Using a combinatorial approach with maps, we prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov. Résumé. Les polynômes de Kerov expriment les valeurs des caractères irréductibles du groupe symmétrique en ...
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We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulants of the Young diagram (certain functionals describing the shape of the Young diagram). We show that for each genus there exists a universal symmetric polynomial which gives the coefficients of the part of Kerov char...
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We give, over a finite field Fq, explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3 · 2, the Dickson polynomials of the first kind of order 3 · 2 and the Dickson polynomials of the second kind of order 3 · 2 − 1.
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In this paper, we make an attempt to study the explicit factorization of 2.7-th cyclotomic polynomials over finite field Fq when q ≡ 1(mod 4) into a product of distinct monic irreducible polynomials, where q is a power of an odd prime. AMS Subject Classification: 11T06, 11T22, 12Y05
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.02.011