Cubical rectangles and rectangular lattices
Abstract
Cubical rectangles are being defined and explored here over the n-dimensional geometric cube Qn. They form a new class of geometric objects that includes all the edges and all the squares of the n-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 n-cube.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.