Infinite tree structure and integer partitions

Phan Ha Duong
Institute of Mathematics, Viet Nam

Abstract
In this paper, we introduce a method called ECO (Enumerating combinatorial objects) to study combinatoric objects, particularly, generating tree for integer partitions. By mean of an operator, able to satisfy two special conditions, we give some recursive structures, and then computing their generating functions. Hence, we present the bijection between the strict partitions and odd partitions. Furthermore, we give some extending results for k-partitions, a generalization of strict partitions.