کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9515469 | 1343457 | 2005 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A method for proving polynomial enumeration formulas
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by “explaining” their zeros using an appropriate combinatorial extension of the objects under consideration to negative integer parameters. We apply this method to prove a new refinement of the Bender-Knuth (ex-)Conjecture, which easily implies the Bender-Knuth (ex-)Conjecture itself. This is probably the most elementary way to prove this result currently known. Furthermore we adapt our method to q-polynomials, which allows us to derive generating function results as well. Finally we use this method to give another proof for the enumeration of semistandard tableaux of a fixed shape which differs from our proof of the Bender-Knuth (ex-)Conjecture in that it is a multivariate application of our method.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 111, Issue 1, July 2005, Pages 37-58
Journal: Journal of Combinatorial Theory, Series A - Volume 111, Issue 1, July 2005, Pages 37-58
نویسندگان
Ilse Fischer,