F-ideals and f-graphs

摘要

For a field K, a square -freemonomialideal I of K x(1), ... , x(n) is calledan f-ideal if bothitsfacetcomplexandStanley -Reisnercomplexhavethesame f-vector. Inthispaper, weintroduceacombinatorialconcept(LU-set) and use ittocharacterizean (n, d) th f-ideal, whoseminimalmonomialgenerating set consistsofsomemonomialsofacommondegree d from K x(1), ... , x(n). Weclassifyall (n, 2)th f -ideals, thuslistall f -graphswhoseedgeidealsare exactlythe (n, 2)th f -ideals. Furthermore, weshowthatall f -graphsareCohen Macaulay.