m at h . G M ] 2 8 Ju n 20 06 Combinatorial Speculations and ̧ the Combinatorial Conjecture for Mathematics ̧
نویسنده
چکیده
¸ maolinfan@163. com¸Abstract : Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an even more important work for mathematician is to apply combinatorics to other mathematics and other sciences beside just to find combinatorial behavior for objectives. In the past few years, works of this kind frequently appeared on journals for mathematics and theoretical physics for cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics, such as those of multi-spaces, map geometries and combinatorial cos-moses, also the combinatorial conjecture for mathematics proposed by myself in 2005. Some open problems are included for the advance of 21th mathematics by a combinatorial speculation. 1. The role of classical combinatorics in mathematics Modern science has so advanced that to find a universal genus in the society of sciences is nearly impossible. Thereby a scientist can only give his or her contribution in one or several fields. The same thing also happens for researchers in combinatorics. Generally, combinatorics deals with twofold: Question 1.1. to determine or find structures or properties of configurations, such as those structure results appeared in graph theory, combinatorial maps and design theory,..., etc.. Question 1.2. to enumerate configurations, such as those appeared in the enu-meration of graphs, labelled graphs, rooted maps, unrooted maps and combinatorial Consider the contribution of a question to science. We can separate mathematical 1
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