Specializations of indecomposable polynomials
نویسندگان
چکیده
منابع مشابه
Specializations of indecomposable polynomials
We address some questions concerning indecomposable polynomials and their behaviour under specialization. For instance we give a bound on a prime p for the reduction modulo p of an indecomposable polynomial P (x) ∈ Z[x] to remain indecomposable. We also obtain a Hilbert like result for indecomposability: if f(t1, . . . , tr, x) is an indecomposable polynomial in several variables with coefficie...
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Three specializations of a set of orthogonal polynomials with “8 different q’s” are given. The polynomials are identified as q-analogues of Laguerre polynomials, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
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We address some questions concerning indecomposable polynomials and their spectrum. How does the spectrum behave via reduction or specialisation, or via a more general ring morphism? Are the indecomposability properties equivalent over a field and over its algebraic closure? How many polynomials are decomposable over a finite field?
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Let K be a number field, and let λ(x, t) ∈ K[x, t] be irreducible over K(t). Using algebraic geometry and group theory, we study the set of α ∈ K for which the specialized polynomial λ(x, α) is K-reducible. We apply this to show that for any fixed n ≥ 10 and for any number field K, all but finitely many K-specializations of the degree n generalized Laguerre polynomial L (t) n (x) are K-irreduci...
متن کاملResearch Statement: Specializations of Macdonald polynomials
Symmetric functions are vital to the study of combinatorics because they provide valuable information about partitions and permutations, topics which constitute the core of the subject. The significance of symmetric function theory is manifest by its connections to other branches of mathematics, including group theory, representation theory, Lie algebras, and algebraic geometry. One important b...
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ژورنال
عنوان ژورنال: Manuscripta Mathematica
سال: 2011
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-011-0520-3