The two-parameter class of Schröder inversions

J. Schröder

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 1, page 5-19
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Schröder, J.. "The two-parameter class of Schröder inversions." Commentationes Mathematicae Universitatis Carolinae 54.1 (2013): 5-19. <http://eudml.org/doc/252495>.

@article{Schröder2013,
abstract = {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.},
author = {Schröder, J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {generalized Schröder numbers; coordination numbers; crystal ball numbers; stretched Riordan array; triangular matrix; sequence transformation; inversion; left-inverse; generalized Schröder numbers; coordination number; crystal ball number; stretched Riordan array; triangular matrix; sequence transformation; inversion},
language = {eng},
number = {1},
pages = {5-19},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The two-parameter class of Schröder inversions},
url = {http://eudml.org/doc/252495},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Schröder, J.
TI - The two-parameter class of Schröder inversions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 1
SP - 5
EP - 19
AB - 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.
LA - eng
KW - generalized Schröder numbers; coordination numbers; crystal ball numbers; stretched Riordan array; triangular matrix; sequence transformation; inversion; left-inverse; generalized Schröder numbers; coordination number; crystal ball number; stretched Riordan array; triangular matrix; sequence transformation; inversion
UR - http://eudml.org/doc/252495
ER -

References

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