Three Notes on Distributive Lattices

On the Homology of Distributive Lattices

✍ W.F. Doran IV 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 167 KB

This paper gives a method for computing the reduced poset homology of the rank-selected subposet of a distributive lattice. As an example of the method, let L be the lattice S b acts on L by permuting coordinates. For S ⊆ [ab], we give a description of the decomposition of the reduced homology of L

Notes on Distributive Groupoids

✍ Tomáš Kepka; Petr Nêmec 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 489 KB

The theory of distributive groupoids and quasigroups seems to be one of those rare cmes of non-associative theories which admit interesting and deep structural results. The complete list of articles on this subject contains relatively many items (an incomplete one is included in the bibliography of

A Note on Optimal Unimodular Lattices

✍ J.H Conway; N.J.A Sloane 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 169 KB

The highest possible minimal norm of a unimodular lattice is determined in dimensions n 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8.10 20 in dimension 33). Unimodular lattices with no roots exist if and only if n 23, n{25

Hypertelorism. Notes on three cases

✍ H. P. Pickerill 📂 Article 📅 1939 🏛 John Wiley and Sons 🌐 English ⚖ 307 KB

Functions on Distributive Lattices with

Functions on Distributive Lattices with the Congruence Substitution Property: Some Problems of Grätzer from 1964

✍ Jonathan David Farley 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 305 KB

Let L be a bounded distributive lattice. For k 1, let S k (L) be the lattice of k-ary functions on L with the congruence substitution property (Boolean functions); let S(L) be the lattice of all Boolean functions. The lattices that can arise as S k (L) or S(L) for some bounded distributive lattice L

A Note on lattices of euclidean subspace

A Note on lattices of euclidean subspaces

✍ Ton Geerts 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 256 KB

Any nonvoid lattice of subspaces from R" is known to be a complete lattice, and hence it has a largest and smallest element. Here we show that for a specific class of subspaces also the converse is true. If this class has a largest and a smallest element, then it is a complete lattice. Within the co