Positive definite matrices and Catalan numbers
Authors: Frank Thomson Leighton and Morris Newman
Journal: Proc. Amer. Math. Soc. 79 (1980), 177-181
MSC: Primary 15A36; Secondary 05A15, 15A48
MathSciNet review: 565333
Abstract: It is shown that the number of integral triple diagonal matrices which are unimodular, positive definite and whose sub and super diagonal elements are all one, is the Catalan number . More generally, it is shown that if A is a fixed integral symmetric matrix and d is a fixed positive integer, then there are only finitely many integral diagonal matrices D such that is positive definite and .
Keywords: Catalan number, congruence, determinant, integer matrix, positive definite matrix, triple diagonal matrix, unimodular matrix
Article copyright: © Copyright 1980 American Mathematical Society