# Ranked poset > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Ranked_poset > Markdown URL: https://mediated.wiki/source/Ranked_poset.md > Source: https://en.wikipedia.org/wiki/Ranked_poset > Source revision: 1256191785 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Partially ordered set in Mathematics}} In [mathematics](/source/mathematics), a '''ranked poset''' is a [partially ordered set](/source/partially_ordered_set) in which one of the following (non-equivalent) conditions hold: it is * a [graded poset](/source/graded_poset), or * a poset with the property that for every element ''x'', all maximal [chains](/source/chain_(order_theory)) among those with ''x'' as [greatest element](/source/greatest_element) have the same finite [length](/source/Glossary_of_order_theory), or * a poset in which all maximal chains have the same finite length. The second definition differs from the first in that it requires all minimal elements to have the same rank; for posets with a least element, however, the two requirements are equivalent. The third definition is even more strict in that it excludes posets with infinite chains and also requires all maximal elements to have the same rank. [Richard P. Stanley](/source/Richard_P._Stanley) defines a graded poset of length ''n'' as one in which all maximal chains have length ''n''.Richard Stanley, ''Enumerative Combinatorics,'' vol.1 p.99, Cambridge Studies in Advanced Mathematics 49, Cambridge University Press, 1995, {{isbn|0-521-66351-2}} == References == {{Reflist|1}} Category:Order theory {{combin-stub}} --- Adapted from the Wikipedia article [Ranked poset](https://en.wikipedia.org/wiki/Ranked_poset) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Ranked_poset?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.