Bourque-Ligh Conjecture

Bourque and Ligh (1992) conjectured that the least common multiple matrix on a GCD-closed set  is nonsingular. This conjecture was shown to be false by Haukkanen et al. (1997) and subsequently by Hong (1999).

REFERENCES:

Bourque, K. and Ligh, S. "On GCD and LCM Matrices." Linear Algebra Appl. 174, 65-74, 1992.

Haukkanen, P.; Wang, J.; and Sillanpää, J. "On Smith's Determinant." Linear Alg. Appl. 258, 251-269, 1997.

Hong, S. "On the Bourque-Ligh Conjecture of Least Common Multiple Matrices." J. Algebra 218, 216-228, 1999.