✦ LIBER ✦
Quasi-Differential Posets and Cover Functions of Distributive Lattices: I. A Conjecture of Stanley
✍ Scribed by Jonathan David Farley
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 532 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
✦ Synopsis
A distributive lattice L with 0 is finitary if every interval is finite. A function f : N 0 Ä N 0 is a cover function for L if every element with n lower covers has f (n) upper covers. In this paper, all finitary distributive lattices with non-decreasing cover functions are characterized. A 1975 conjecture of Richard P. Stanley is thereby settled.