BCK/BCI algebras are two classes of logic algebras. Previous studies have enriched the relevant theories about that. Some researchers have solved the counting problem of BCI algebras with less than six elements. But the counting problem of general BCI algebra is still unsolved. In this paper, the definition about the coset of BCI-algebra will be given. And some characters about the cosets on some particular sub-algebras will be studied. Finally, the cosets of right-eliminable BCI-algebras will be studied. A theorem about counting BCI-algebra will be given.
The four-colour problem came from the practice of drawing maps. It was called the four-color conjecture before it is proved. This paper, attempts to simplify this problem to some extent and gives a simplified proof. Finally, the expected results are obtained. In the process, two theorems which can be used to simplify vertex colouring problems are also obtained.
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