一个新的Kempe不变量和Wang-Swendsen-Kotecky算法的（非）遍历性
A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm
摘要：
我们证明了对于闭定向曲面的三色三角剖分类，四色模12的度在Kempe变换下是不变的。利用这个一般性结果证明了：对于环面的所有三角剖分T（3L，3 M），当3<= L <= M时，至少存在两个Kempe等价类.这个结果特别意味着零温四态Potts反铁磁体在环面三角剖分T（3L，3 M）上的Wang-Swendsen-Kotecky算法不是遍历的。
英文摘要：
We prove that for the class of three-colorable triangulations of a closed oriented surface, the degree of a four-coloring modulo 12 is an invariant under Kempe changes. We use this general result to prove that for all triangulations T(3L,3M) of the torus with 3<= L <= M, there are at least two Kempe equivalence classes. This result implies in particular that the Wang-Swendsen-Kotecky algorithm for the zero-temperature 4-state Potts antiferromagnet on these triangulations T(3L,3M) of the torus is not ergodic.
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