On the H-triangle of generalised nonnesting partitions

作者：Thiel Marko^*

来源：European Journal of Combinatorics, 2014, 39: 244-255.

DOI：10.1016/j.ejc.2014.01.010

With a crystallographic root system Phi and a positive integer k, there are associated two Fu-Catalan objects, the set of k-generalised nonnesting partitions NN(k)(Phi), and the generalised cluster complex Delta((k))(Phi). These possess a number of enumerative coincidences, many of which are captured in a surprising identity, first conjectured by Chapoton for k = 1 and later generalised to k >= 1 by Armstrong. We prove this conjecture, obtaining some structural and enumerative results on NN(k)(Phi) along the way, including an earlier conjecture by Fomin and Reading giving a refined enumeration by Fuss-Narayana numbers.

• 出版日期2014-7