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Abstract
The goal of the present work is to enumerate polyominoes of minimal area
plus one inscribed in a rectangle by combinatorial methods. In the first chapter,
1 present the definitions and classifications of polyominoes and a brief
generalization of polyominoes of minimal area. Then, in chapter two 1 describe
the algebra of ordinary and exponential generating functions and ,a
tool that serves to explain the exact enumerative formulas for polyominoes
of minimal area and minimum area plus one treated in the chapter three. In
chapter three, we develop a combinatorial method for enumerating polyominoes
of minimal area plus one ; their generating series, their generalization,
their exact enumeration formulas and sorne applications. This chapter is a review
of a document, written by my dissertation advisor, on the enumeration
of inscribed polyominoes.
And finally, in chapter four , 1 present the algorithm that generates the main
program and polyominoes without cycles and the source code. This program
was used as a database to check the exact formulas presented in this mas ter
thesis.