Cubical rectangles and rectangular lattices
Combinatorics
2023-06-12 v2
Abstract
Cubical rectangles are being defined and explored here over the dimensional geometric cube They form a new class of geometric objects that includes all the edges and all the squares of the cube. We enumerate and characterize them here in order to construct new posets, transforming into special lattices that will be called rectangular lattices. We show that rectangular lattices are closely related to the class of cubical lattices, that is, the face lattice of the cube.
Cite
@article{arxiv.1803.10667,
title = {Cubical rectangles and rectangular lattices},
author = {M. Reza Emamy-K},
journal= {arXiv preprint arXiv:1803.10667},
year = {2023}
}
Comments
The last theorem of the paper (Theorem 6) must be revised, the way it is presented is not completely correct