Abstract
Given a family of sets L, where the sets in L admit k 'degrees of freedom', we prove that not all (k+1)-dimensional posets are containment posets of sets in L. Our results depend on the following enumerative result of independent interest: Let P(n, k) denote the number of partially ordered sets on n labeled elements of dimension k. We show that log P(n, k)∼nk log n where k is fixed and n is large.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 11-16 |
| Number of pages | 6 |
| Journal | Order |
| Volume | 5 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 1988 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics
Keywords
- AMS subject classifications (1980): 06A10 (primary), 14N10 (secondary)
- Partially ordered set
- containment order
- degrees of freedom
- partial order dimension
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