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An elegant procedure which characterizes a decomposition of some class ofbinomial configurations into two other, resembling a definition of Pascal'sTriangle, was given in \cite{gevay}. In essence, this construction was alreadypresented in \cite{perspect}. We show that such a procedure is a result offixing in configurations in some class $\mathcal K$ suitable hyperplanes whichboth: are in this class, and deleting such a hyperplane results in aconfiguration in this class. By a way of example we show two more (added tothat of \cite{gevay}) natural classes of such configurations, discuss someother, and propose some open questions that seem also natural in this context.

Hyperplanes in Configurations, decompositions, and Pascal Triangle of Configurations