Journal of Integer Sequences, Vol. 4 (2001), Article 01.1.2

Hankel Matrices and Lattice Paths

Wen-Jin Woan
Department of Mathematics
Howard University
Washington, D.C. 20059, USA

Email address:

Abstract: Let H be the Hankel matrix formed from a sequence of real numbers S = {a0 = 1, a1, a2, a3, ...}, and let L denote the lower triangular matrix obtained from the Gaussian column reduction of H. This paper gives a matrix-theoretic proof that the associated Stieltjes matrix SL is a tri-diagonal matrix. It is also shown that for any sequence (of nonzero real numbers) T = {d0 = 1, d1, d2, d3, ...} there are infinitely many sequences such that the determinant sequence of the Hankel matrix formed from those sequences is T.

Full version:  pdf,    ps,    dvi,    latex,   

(Mentions sequences A000108 A001006 A001850.)

Received September 19 2000; published in Journal of Integer Sequences, April 24 2001.

Return to Journal of Integer Sequences home page