Representation of ordered trees with a given degree distribution

The degree distribution of an ordered tree T with n nodes is vecn = (n0,ldots,nn-1), where ni is the number of nodes in T with i children. Let N(vecn) be the number of trees with degree distribution vecn. We give a data structure that stores an ordered tree T with n nodes and degree distribution vecn using log N(vecn)+O(n/logt n) bits for every constant t. The data structure answers tree queries in constant time. This improves the current data structures with lowest space for ordered trees: The structure of Jansson et al. [JCSS 2012] that uses logN(vecn)+O(nloglog n/log n) bits, and the structure of Navarro and Sadakane [TALG 2014] that uses 2n+O(n/logt n) bits for every constant t.