pure poset

A poset is pure if it is finite and every maximal chain has the same length.If P is a pure poset, we can create a rank function r on P by definingr(x) to be the length of a maximal chain bounded above by x. Everyinterval of a pure poset is a graded poset, and every graded poset is pure. Moreover,the closure of a pure poset, formed by adjoining an artificial minimum element andan artificial maximum element, is always graded.

The face poset of a pure simplicial complex is pure as a poset.

单词	PurePoset
释义	pure poset A poset is pure if it is finite and every maximal chain has the same length.If P is a pure poset, we can create a rank function r on P by definingr(x) to be the length of a maximal chain bounded above by x. Everyinterval of a pure poset is a graded poset, and every graded poset is pure. Moreover,the closure of a pure poset, formed by adjoining an artificial minimum element andan artificial maximum element, is always graded. The face poset of a pure simplicial complex is pure as a poset.
随便看	SchinzelsTheorem Schinzel’s Hypothesis H Schinzel’s theorem SchlichtFunctions schlicht functions SchnirelmannDensity Schnirelmann density SchockPrize Schock Prize SchootenTheorem Schooten theorem SchreierDomain Schreier domain SchreierIndexFormula Schreier index formula SchreierRefinementTheorem Schreier refinement theorem SchreiersLemma Schreier’s lemma SchroderBernsteinTheorem SchroderBernsteinTheoremProof SchrodingerOperator SchrodingersWaveEquation SchroederBernsteinTheoremProofOf Schroeder-Bernstein theorem, proof of