کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4657551 | 1343751 | 2006 | 50 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Polynomial equations with one catalytic variable, algebraic series and map enumeration
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let F(t,u)≡F(u)F(t,u)≡F(u) be a formal power series in t with polynomial coefficients in u . Let F1,…,FkF1,…,Fk be k formal power series in t, independent of u. Assume all these series are characterized by a polynomial equationP(F(u),F1,…,Fk,t,u)=0.P(F(u),F1,…,Fk,t,u)=0. We prove that, under a mild hypothesis on the form of this equation, these k+1k+1 series are algebraic, and we give a strategy to compute a polynomial equation for each of them. This strategy generalizes the so-called kernel method and quadratic method , which apply, respectively, to equations that are linear and quadratic in F(u)F(u). Applications include the solution of numerous map enumeration problems, among which the hard-particle model on general planar maps.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 96, Issue 5, September 2006, Pages 623–672
Journal: Journal of Combinatorial Theory, Series B - Volume 96, Issue 5, September 2006, Pages 623–672
نویسندگان
Mireille Bousquet-Mélou, Arnaud Jehanne,