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- W2740807620 abstract "Consider all possible oriented Hamiltonian cycles over the vertices of a regular n-gon, where n ∈ N, n ≥ 3. The main aim of this note is to count the cycles which are not equivalent under the rotations of the n-gon. It is well known when n is a prime number the number of simple cycles is |HCn| = n− 2 + (n− 1)! + 1 n , so the above counting problem leads to the classical Wilson’s theorem. We count the nonequivalent cycles for the case of an arbitrary natural number n, so the obtained congruences can be viewed as natural generalizations of Wilson’s theorem. The same results were obtained recently by T.J. Evans using the Burnside theorem for counting the number of orbits of a group action. Our method uses an argument by function iteration and leads to some additional congruences." @default.
- W2740807620 created "2017-08-08" @default.
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- W2740807620 date "2011-01-01" @default.
- W2740807620 modified "2023-09-24" @default.
- W2740807620 title "A combinatorial generalization of Wilson's theorem." @default.
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