Statistics on non-crossing trees

Combinatorial Statistics on Non-crossing Partitions

Four statistics, ls, rb, rs, and lb, previously studied on all partitions of { 1, 2, ..., n }, are applied to non-crossing partitions. We consider single and joint distributions of these statistics and prove equidistribution results. We obtain qand p, q-analogues of Catalan and Narayana numbers which refine the rank symmetry and unimodality of the lattice of non-crossing partitions. Two unimoda...

Extremal statistics on non-crossing configurations

We analyze extremal statistics in non-crossing configurations on the n vertices of a convex polygon.We prove that themaximumdegree and the largest component are of logarithmic order, and that, suitably scaled, they converge to a well-defined constant. We also prove that the diameter is of order √ n. The proofs are based on singularity analysis, an application of the first and second moment meth...

Edge Operations on Non-Crossing Spanning Trees

Pattern Avoidance in Generalized Non-crossing Trees

Abstract. In this paper, the problem of pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding patterns of length one and two are obtained. Lagrange inversion formula is used to obtain the explicit formulas for some special cases. Bijection is also established between generalized non-crossing trees with special patter...

Multichains, non-crossing partitions and trees

In a previous paper El], we proved results -about the enumer;ation of certain types of chains in the non-crossing partition lattice T, and its, generalizations. In this paper we present bijections to certain classes of trees which reprove one theorem [l, Corollary 3.41 and provide a combinatoridi proof for the other [I, Theorem 5.31. We begin with a review of the definitions. A set partition X ...