GCD闭集上的LCM矩阵

LCM Matrices on GCD-Closed Sets

１９９２年Ｂｅｓｌｉｎ和Ｌｉｇｈ讨论了ＧＣＤ矩阵在ＧＣＤ闭集上的种种结果，并引入了所谓Ｋ－集的概念本文中，作者们将讨论一类所谓ＬＣＭ矩阵在ＧＣＤ闭集上的各种结果．我们给出了结构定理、行列式的计算公式，最后，当集合Ｓ为Ｋ－集时，我们得出了行列式计算的封闭型表达式，从而全面推广了他们的结果．

In this paper, we generalized the resutls given by Beslin & Lign. The resutls on GCD matrices defined on GCD-closed sets are extended to that of LCM matrices defined on GCD-closed sets. The structure theorem for LCM matrices is obtained. We give a formula for calculating the determinant of LCM matrices on GCD - closed sets. Finally a few formulas about so-called K-sets are given.