Geodesic
Hankel matrices and lattice paths
Journal of integer sequences, Tome 4 (2001) no. 1
Let H be the Hankel matrix formed from a sequence of real numbers S = a_0 = 1, a_1, a_2, a_3, $\dots $, 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 S_L is a tri-diagonal matrix. It is also shown that for any sequence (of nonzero real numbers) T = d_0 = 1, d_1, d_2, d_3, $\dots $ there are infinitely many sequences such that the determinant sequence of the Hankel matrix formed from those sequences is T.
Classification : 15B57, 11B83, 11C20
Mots-clés : Hankel matrices, lattice paths, Gaussian column reduction, Stieltjes matrix, determinant sequence 
@article{JIS_2001__4_1_a4,
     author = {Woan,  Wen-Jin},
     title = {Hankel matrices and lattice paths},
     journal = {Journal of integer sequences},
     year = {2001},
     volume = {4},
     number = {1},
     zbl = {0978.15021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2001__4_1_a4/}
}
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Woan,  Wen-Jin. Hankel matrices and lattice paths. Journal of integer sequences, Tome 4 (2001) no. 1. http://geodesic.mathdoc.fr/item/JIS_2001__4_1_a4/