| 摘 要： | In the paper“The equitype and quasi-equitype decompositions of arbitrarypermutation by permutations of order 2 or 3”,we proved that any even permu-tation can be expressed as a product of two equitype involutions and any odd per-mutation can be expressed as a product of two quasi-equitype involutions. Meanwh-ile,we gave the condition on t such that an even permutation has(2~t)equitypedecompositions and the condition on t such that an odd permutation has(2;2~t)quasi-equitype decompositions.In this paper,we give the numbers of the equitypeand quasi-equitype decompositions of a permutation.The main results are
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