Heesung Shin

Annular noncrossing permutations and minimal transitive factorizations

We give a combinatorial proof of Goulden and Jacksons formula for the number of minimal transitive factorizations of a permutation when the permutation has two cycles. We use the recent result of Goulden, Nica, and Oancea on the number of maximal chains of annular noncrossing partitions of type B.

A REFINEMENT FOR ORDERED LABELED TREES

Let

Enumerations of vertices among all rooted ordered trees with levels and degrees

\mathcal{O}_n

Colored Prufer codes for k-edge colored trees

be the set of ordered labeled trees on

On the enumeration of rooted trees with fixed size of maximal decreasing trees

{0,...,n}

SIGNED A-POLYNOMIALS OF GRAPHS AND POINCARÉ POLYNOMIALS OF REAL TORIC MANIFOLDS

. A maximal decreasing subtree of an ordered labeled tree is defined by the maximal ordered subtree from the root with all edges being decreasing. In this paper, we study a new refinement

Another refinement for Rooted Trees

\mathcal{O}_{n,k}

Refined enumeration of vertices among all rooted ordered

of

d

\mathcal{O}_n

-trees

, which is the set of ordered labeled trees whose maximal decreasing subtree has