Hyperplanes in Configurations, decompositions, and Pascal Triangle of Configurations
Combinatorics
2019-07-23 v1
Abstract
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 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.
Cite
@article{arxiv.1907.09165,
title = {Hyperplanes in Configurations, decompositions, and Pascal Triangle of Configurations},
author = {Krzysztof Prażmowski},
journal= {arXiv preprint arXiv:1907.09165},
year = {2019}
}