A generalized enumeration of labeled trees and reverse Prüfer algorithm
نویسندگان
چکیده
A leader of a tree T on [n] is a vertex which has no smaller descendants in T . Gessel and Seo showed that ∑ T ∈Tn u(# of leaders in T )c(degree of 1 in T ) = uPn−1(1, u, cu), which is a generalization of Cayley’s formula, where Tn is the set of trees on [n] and Pn(a, b, c)= c n−1 ∏ i=1 ( ia + (n− i)b+ c. Using a variation of the Prüfer code which is called a RP-code, we give a simple bijective proof of Gessel and Seo’s formula. © 2007 Elsevier Inc. All rights reserved.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 114 شماره
صفحات -
تاریخ انتشار 2007