English

Cubical rectangles and rectangular lattices

Combinatorics 2023-06-12 v2

Abstract

Cubical rectangles are being defined and explored here over the nn-dimensional geometric cube Qn.Q_n. They form a new class of geometric objects that includes all the edges and all the squares of the nn-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 nn-cube.

Keywords

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