Combinatorial arabesque : a new concept

الملخص EN

This paper is interefled in developing a new application in combinatorial analysis, which will be called “combinatorial arabesque”.

There are many disciplines, which have a relationship with analytic combinatorics such as “Graph theory”, “combinatorial optimization” and “Probabiliflic combinatorics”.

However, applying combinatorial analysis on geometric patterns is actually a new topic and there is no previous fludy on this subject.

This topic seems to be a simple composition of geometrical patterns, but it really uses many branches of mathematics such as counting techniques, analysis, and flructural algebra related to geometric transformations.

The results of this paper is two tenors, the firfl is mathematical by determining all of the specific kind of motifs that shall be called “Entirely symmetrical motifs”.

The second tenor is artiflic and decorative by contracting beautiful motif from ugly one.

Finally, a mathematical definition of beauty degree of a motif is given.