[{"type":"report","title":"Set systems related to a house allocation problem","issued":{"date-parts":[["2020","7"]]},"author":[{"family":"Gerbner","given":"D\u00e1niel"},{"family":"Keszegh","given":"Bal\u00e1zs"},{"family":"Methuku","given":"Abhishek"},{"family":"Nagy","given":"D\u00e1niel T."},{"family":"Patk\u00f3s","given":"Bal\u00e1zs"},{"family":"Tompkins","given":"Casey"},{"family":"Xiao","given":"Chuanqi"}],"abstract":"We are given a set A of buyers, a set B of houses, and for each buyer a preference list, i.e., an ordering of the houses. A house allocation is an injective mapping \u03c4 from A to B, and \u03c4 is strictly better than another house allocation \u03c4\u2032\u2260\u03c4 if for every buyer i, \u03c4\u2032(i) does not come before \u03c4(i) in the preference list of i. A house allocation is Pareto optimal if there is no strictly better house allocation.\r\nLet s(\u03c4) be the image of \u03c4 (i.e., the set of houses sold in the house allocation \u03c4). We are interested in the largest possible cardinality f(m) of the family of sets s(\u03c4) for Pareto optimal mappings \u03c4 taken over all sets of preference lists of m buyers. We improve the earlier upper bound on f(m) given by Asinowski, Keszegh and Miltzow by making a connection between this problem and some problems in extremal set theory.","kit-publication-id":"1000124780"}]