Timeline for Terminology and technique for repeated pairwise removal of elements of posets: "Collapsibility" of a "face poset"

7 events

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May 10, 2016 at 22:06	comment	added	gksato		In fact, in case of ranked posets (=all maximal chains has the same finite length), $P$ must have Euler characteristic 1.
May 10, 2016 at 14:55	comment	added	gksato		No. It is NOT collapsible. and yes,that's very important necessary condition.
May 10, 2016 at 12:45	comment	added	Dominic van der Zypen		Is the poset $P=\{0,1\}$ ordered by $0<1$ collapsible? As I understand $(1,0)$ is a maximal pair, but $P \setminus\{1,0\} = \emptyset \neq \{*\}$ as you demand. - If I understand correctly, one simple criterion for $P$ to be collapsible is that it has an odd number of points in the base set.
May 7, 2016 at 9:42	comment	added	gksato		Note that: $P'=P\setminus\left\{u,v\right\}$. And $v$ must be maximal in $P\setminus \left\{ u \right\} $. So $\left\{x > y < z\right\}$ (in which x and z are incomparable) is not collapsible.
May 7, 2016 at 9:36	comment	added	Asaf Karagila♦		So you have a finite partial order, and you just remove maximal elements one by one (each time maximal in the "collapsed" order) until you've cleared up the entire thing. What am I missing? Also what does $v$ matter in the choice of collapsing the order? You just remove $u$ which is a maximal element, and that's it.
May 7, 2016 at 7:10	review	First posts
May 7, 2016 at 8:10
May 7, 2016 at 7:08	history	asked	gksato	CC BY-SA 3.0