Polymake for complete matching polytope for complete graph CAVEATS ------------------------------------ 1) Note that if you are using the browser-based polymake like me (http://shell.polymake.org/) you can copy from my stuff and paste into the browser by right-clicking. Be careful though because your browser/clipboard may insert line breaks, which mess it up for a big entry. Paste into notepad first and remove them. 2) I left the prompt “polytope >” in. Remove this. 3) Underscores like in F_VECTOR get removed sometimes and need replaced. Can be done in the pasting box in polymake. 4) I put the required initial “1” in each point. ------------------------------------ INPUT/OUTPUT n = 3 ------------------------------------ polytope > $points=new Matrix([[1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0],[1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0],[1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0],[1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0],[1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0],[1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0],[1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0]]); polytope > $p=new Polytope(POINTS=>$points); polytope > print $p->F_VECTOR; 15 105 435 1095 1657 1470 735 195 25