%0 Journal Article %T Minimal Number of Edges in Hypergraph Guaranteeing Perfect Fractional Matching and MMS Conjecture %A Vladimir Blinovsky %J Mathematics %D 2013 %I arXiv %X We prove Ahlswede- Khachatrian conjecture. From this conjecture follows of several other conjectures including Manickam-Mikl\'{o}s-Singhi conjecture. %U http://arxiv.org/abs/1310.0989v5