The motif problem
Combinatorics
2012-10-26 v1
Abstract
Fix a choice and ordering of four pairwise non-adjacent vertices of a parallelepiped, and call a motif a sequence of four points in R^3 that coincide with these vertices for some, possibly degenerate, parallelepiped whose edges are parallel to the axes. We show that a set of r points can contain at most r^2 motifs. Generalizing the notion of motif to a sequence of L points in R^p, we show that the maximum number of motifs that can occur in a point set of a given size is related to a linear programming problem arising from hypergraph theory, and discuss some related questions.
Cite
@article{arxiv.1210.6667,
title = {The motif problem},
author = {E. Rodney Canfield and Ron Fertig and R. Daniel Mauldin and David Moews},
journal= {arXiv preprint arXiv:1210.6667},
year = {2012}
}
Comments
17 pages, 1 figure