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Vietnam Journal of Mathematics 37:2&3 (2009) 273-293 

Integer Partitions in Discrete Dynamical Models and ECO Method

Le Manh Ha and Phan Thi Ha Duong

Abstract.  In this paper, we study general types of integer partitions as configurations of discrete dynamical models with two transition rules and with the initial configuration being the singleton partition. This allows us to characterize its lattice structure, fixed point, and the recursive structure of the infinite extension of the lattice of these partitions. Besides, we use ECO method (Enumeration combinatorial objects) independently to study generating trees for integer partitions. By means of an operator satisfying two special conditions, we give some recursive structures which are exactly the same to those studied from the point of view of discrete dynamical systems. We also calculate their generating functions and present the bijection between the strict partitions and odd partitions.

2000 Mathematics Subject Classification: Primary 05A17, 05A19. Secondary 37E17, 68R05.

Keywords: Integer partition, ECO method, generating tree, generating function, Discrete dynamical system.

 

 

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