کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4653595 | 1632783 | 2014 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Disposition polynomials and plane trees
ترجمه فارسی عنوان
توزیع چندجملهای و درختان هواپیما
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
We define the disposition polynomial Rm(x1,x2,â¦,xn) as âk=0mâ1(x1+x2+â¯+xn+k). When m=nâ1, this polynomial becomes the generating function of plane trees with respect to the number of younger children and the number of elder children obtained by Guo and Zeng. They asked for a combinatorial proof of the formula. We find a combinatorial interpretation of the disposition polynomials in terms of the number of right-to-left minima of each linear order in a disposition. Then we establish a bijection between plane trees on n vertices and dispositions from {1,2,â¦,nâ1} to {1,2,â¦,n} in the spirit of the Prüfer correspondence, which gives an answer to the question of Guo and Zeng. This bijection also provides an answer to another question of Guo and Zeng concerning an identity on the plane tree expansion of a polynomial introduced by Gessel and Seo.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 36, February 2014, Pages 122-129
Journal: European Journal of Combinatorics - Volume 36, February 2014, Pages 122-129
نویسندگان
William Y.C. Chen, Janet F.F. Peng,