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Combinatorial Arabesque: A new concept

This paper is interested 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 “Probabilistic combinatorics”. However, applying combinatorial analysis on geometric patterns is actually a new topic and there is no previous study 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 structural algebra related to geometric transformations. The results of this paper is two tenors, the first is mathematical by determining all of the specific kind of motifs that shall be called “Entirely symmetrical motifs”. The second tenor is artistic and decorative by constructing beautiful motif from ugly one. Finally, a mathematical definition of beauty degree of a motif is given.