Name
Abstract | ||
|---|---|---|
Let P and Q be finite partially ordered sets on d = { 1 , ¿ , d } , and O ( P ) ¿ R d and O ( Q ) ¿ R d their order polytopes. The twinned order polytope of P and Q is the convex polytope Δ ( P , - Q ) ¿ R d which is the convex hull of O ( P ) ¿ ( - O ( Q ) ) . It follows that the origin of R d belongs to the interior of Δ ( P , - Q ) if and only if P and Q possess a common linear extension. It will be proved that, when the origin of R d belongs to the interior of Δ ( P , - Q ) , the toric ideal of Δ ( P , - Q ) possesses a quadratic Gröbner basis with respect to a reverse lexicographic order for which the variable corresponding to the origin is the smallest. Thus in particular if P and Q possess a common linear extension, then the twinned order polytope Δ ( P , - Q ) is a normal Gorenstein Fano polytope. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.ejc.2015.12.014 | Eur. J. Comb. |
DocType | Volume | Issue |
Journal | 54 | C |
ISSN | Citations | PageRank |
0195-6698 | 2 | 0.46 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Takayuki Hibi | 1 | 94 | 30.08 |
| Kazunori Matsuda | 2 | 2 | 0.46 |