Hyperplanes in Configurations, decompositions, and Pascal Triangle of Configurations

An elegant procedure which characterizes a decomposition of some class of binomial configurations into two other, resembling a definition of Pascal's Triangle, was given in \cite{gevay}. In essence, this construction was already presented in \cite{perspect}. We show that such a procedure is a r...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Author: Prażmowski, Krzysztof
Format: Article
Language:English
Subjects:
Configurations
Decomposition
Hyperplanes
Online Access:Get full text
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Summary:An elegant procedure which characterizes a decomposition of some class of binomial configurations into two other, resembling a definition of Pascal's Triangle, was given in \cite{gevay}. In essence, this construction was already presented in \cite{perspect}. We show that such a procedure is a result of fixing in configurations in some class \(\mathcal K\) suitable hyperplanes which both: are in this class, and deleting such a hyperplane results in a configuration in this class. By a way of example we show two more (added to that of \cite{gevay}) natural classes of such configurations, discuss some other, and propose some open questions that seem also natural in this context.
ISSN:2331-8422