Order, lattices, ordered algebraic structures Chains, antichains, dimension Concept
Height of a poset
Summary
The height of a partially ordered set is the largest number of elements of a chain in it. It is the number of elements in the longest sequence of elements each strictly above the previous one. By Mirsky's theorem, for a finite poset it is also the least number of antichains that cover the poset.
Where this leads
1 page builds on this one.
Further reading
About this page
| Tag | MPR6MH4YSQ |
|---|---|
| URI | m2://MPR6MH4YSQ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A07 |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- an inventory row: the row of the inventory that the node accounts for (0 of 1)
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.