Seunghyun Seo

Enumeration of ( 0 , 1 ) -matrices avoiding some 2 × 2 matrices

We enumerate the number of ( 0 , 1 ) -matrices avoiding 2 i? 2 submatrices satisfying certain conditions. We also provide corresponding exponential generating functions.

Overpartitions and Singular Overpartitions

Singular overpartitions, which were defined by George Andrews, are overpartitions whose Frobenius symbols have at most one overlined entry in each row. In his paper, Andrews obtained interesting combinatorial results on singular overpartitions, one of which relates a certain type of singular overpartition with a subclass of overpartitions. In this paper, we provide a combinatorial proof of Andrews’s result, which answers one of his open questions.

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

Enumeration of partitions with prescribed successive rank parity blocks

\mathcal{O}_n

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

be the set of ordered labeled trees on

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

{0,...,n}

Refined enumeration of vertices among all rooted ordered

. 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

d

\mathcal{O}_{n,k}

-trees

of