题目：A Generalization of the Ramanujan Polynomials and Plane Trees
报告人：郭军伟(法国里昂大学博士后)
时间： 3月28号（星期二）下午1：30-2：30
地点： 理科大楼A1510
摘要:Generalizing a sequence of Lambert, Cayley and Ramanujan, Chapoton has recently introduced a polynomial sequence Q_n:=Q_n(x,y,z,t)
defined by Q_1=1, Q_{n+1}=[x+nz+(y+t)(n+ypartial_y)] Q_n. In this paper we prove Chapoton's conjecture on the duality formula: Q_n(x,y,z,t)=Q_n(x+nz+nt,y,-t,-z), and answer his question about the combinatorial interpretation of Q_n. Actually we give combinatorial interpretations of these polynomials in terms of plane trees, half-mobile trees, and forests of plane trees.Our approach also leads to a general formula that unifies several known results for enumerating trees and plane trees.


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数学系
2006年3月27日