✦ LIBER ✦

Representations of a sublattice of the partition lattice on a lattice

✍ Scribed by Ronny Rousseau

Publisher: Elsevier Science
Year: 1983
Tongue: English
Weight: 529 KB
Volume: 47
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90101-2

No coin nor oath required. For personal study only.

✦ Synopsis

A partial ordering is defined for monotone projections on a lattice, such that the set of these mappings is a lattice which is isomorphic to a sublattice of the partition lattice.

📜 SIMILAR VOLUMES

On sublattices of the hexagonal lattice

✍ M. Bernstein; N.J.A. Sloane; Paul E. Wright 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 404 KB

How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signal-to-noise ratio, or energy? We answer the first question completely and give partial answers to the other questions.

On a representation of lattices

✍ I. Kříz̃; A. Pultr 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 441 KB

On finite elements in sublattices of Ban

On finite elements in sublattices of Banach lattices

✍ Z. L. Chen; M. R. Weber 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 162 KB

## Abstract Let __E__ be a Banach lattice. Let __H__ stand for a sublattice, an ideal or a band in __E__, and denote by Φ~1~(__E__) and Φ~1~(__H__) the ideals of finite elements in the vector lattices __E__ and __H__, respectively. In this paper we first present some sufficient conditions and some

A note on representation of lattices by

A note on representation of lattices by tolerances

✍ Ivan Chajda; Gábor Czédli 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 86 KB

A Representation of Finitely-Modular AC-

A Representation of Finitely-Modular AC-lattices

✍ Jan Hamhalter 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 231 KB

## Abstract We give a lattice‐theoretic characterization of the lattices of Mackey closed subspaces in a vector space __V__ (dim __V__ ≧ 4): These are exactly complete finitely‐modular AC‐lattices of the length at least four which have mutually perspective atoms.

On the structure of the lattice of noncr

On the structure of the lattice of noncrossing partitions

✍ Rodica Simion; Daniel Ullman 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 882 KB

Simion, R. and D. Ullman, On the structure of the lattice of noncrossing partitions, Discrete Mathematics 98 (1991) 193-206. We show that the lattice of noncrossing (set) partitions is self-dual and that it admits a symmetric chain decomposition. The self-duality is proved via an order-reversing i