کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9515327 | 1343446 | 2005 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A direct bijection for the Harer-Zagier formula
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We give a combinatorial proof of Harer and Zagier's formula for the disjoint cycle distribution of a long cycle multiplied by an involution with no fixed points, in the symmetric group on a set of even cardinality. The main result of this paper is a direct bijection of a set Bp,k, the enumeration of which is equivalent to the Harer-Zagier formula. The elements of Bp,k are of the form (μ,Ï), where μ is a pairing on {1,â¦,2p}, Ï is a partition into k blocks of the same set, and a certain relation holds between μ and Ï. (The set partitions Ï that can appear in Bp,k are called “shift-symmetric”, for reasons that are explained in the paper.) The direct bijection for Bp,k identifies it with a set of objects of the form (Ï,t), where Ï is a pairing on a 2(p-k+1)-subset of {1,â¦,2p} (a “partial pairing”), and t is an ordered tree with k vertices. If we specialize to the extreme case when p=k-1, then Ï is empty, and our bijection reduces to a well-known tree bijection.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 111, Issue 2, August 2005, Pages 224-238
Journal: Journal of Combinatorial Theory, Series A - Volume 111, Issue 2, August 2005, Pages 224-238
نویسندگان
I.P. Goulden, A. Nica,