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Vietnam
Journal of Mathematics 37:2&3 (2009) 273-293
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Integer Partitions in Discrete Dynamical Models
and ECO Method
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Le Manh Ha and Phan
Thi Ha Duong
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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.
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2000 Mathematics Subject Classification: Primary 05A17,
05A19. Secondary 37E17, 68R05.
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Keywords: Integer partition, ECO method, generating
tree, generating function, Discrete dynamical system.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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