Local formations in which every subformation of typeNphas a complement

Posets in which every interval is a prod

Posets in which every interval is a product of chains, and natural local actions of the symmetric group

✍ David J. Grabiner 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 545 KB

Consider a graded poset P with maximal and minimal elements. If every interval of rank three in P is a product of chains, and for every interval [.L ~1 of rank at least four, the open interval (x, y) is connected, we show that the entire poset is a product of chains. This proves a conjecture of Stan