Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields

Autor:	Gathen, Joachim von zur, Viola, Alfredo, Ziegler, Konstantin
Rok vydání:	2009
Předmět:	Mathematics - Commutative Algebra Mathematics - Combinatorics 11T06 (Primary) 12Y05 05A15 (Secondary)
Zdroj:	SIAM Journal on Discrete Mathematics 27 (2013) 855-891
Druh dokumentu:	Working Paper
DOI:	10.1137/110854680
Popis:	We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, another one uses a combinatorial method. They yield exact formulas and approximations with relative errors that essentially decrease exponentially in the input size. Comment: to appear in SIAM Journal on Discrete Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0912.3312 Zobrazit plný text záznamu View this record from Arxiv