Geodesic
The two-parameter class of Schröder inversions
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 5-19 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Infinite lower triangular matrices of generalized Schröder numbers are used to construct a two-parameter class of invertible sequence transformations. Their inverses are given by triangular matrices of coordination numbers. The two-parameter class of Schröder transformations is merged into a one-parameter class of stretched Riordan arrays, the left-inverses of which consist of matrices of crystal ball numbers. Schröder and inverse Schröder transforms of important sequences are calculated.
Infinite lower triangular matrices of generalized Schröder numbers are used to construct a two-parameter class of invertible sequence transformations. Their inverses are given by triangular matrices of coordination numbers. The two-parameter class of Schröder transformations is merged into a one-parameter class of stretched Riordan arrays, the left-inverses of which consist of matrices of crystal ball numbers. Schröder and inverse Schröder transforms of important sequences are calculated.
Classification : 05A10, 05A15, 05A19
Keywords: generalized Schröder numbers; coordination numbers; crystal ball numbers; stretched Riordan array; triangular matrix; sequence transformation; inversion; left-inverse 
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     title = {The two-parameter class of {Schr\"oder} inversions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Schröder, Joachim. The two-parameter class of Schröder inversions. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/CMUC_2013_54_1_a1/