F闭集上的LCM矩阵

LCM Matrices on Factor-Closed Sets

本文将定义在集Ｓ上的最大公因子（ＧＣＤ）矩阵〔Ｇ（Ｓ）〕推广到Ｓ上的最小公倍（ＬＣＭ）矩阵〔Ｌ（Ｓ）〕．我们给出了矩阵〔Ｌ（Ｓ）〕的结构定理以及行列式ｄｅｔ〔Ｌ（Ｓ）〕的计算公式．当Ｓ为因子闭集时，我们给出了行列式ｄｅｔ〔Ｌ（Ｓ）〕的一个简洁优美的公式．

This paper extends the greatest common divisor (GCD)mstrixG(S)]dafined on S to the least common multiple (LCM)matrix[L(S)] defined on a set S.The structure theorem for[L(S)] is obtained. We give a formula for computing det[L(S)]. When S is Factor-closed, a simple and elegant formula for det[L(S)]is given.