## 44 Citations

### On 2-regular $k$-noncrossing partitions

- Mathematics
- 2007

In this paper we prove a bijection between 2-regular, $k$-noncrossing partitions and $k$-noncrossing enhanced partitions. Via this bijection we enumerate 2-regular, 3-noncrossing partitions using an…

### A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions

- MathematicsDiscret. Math.
- 2020

### Enumeration of Gap-Bounded Set Partitions

- MathematicsJ. Autom. Lang. Comb.
- 2009

We count set partitions in which the gaps between adjacent elements in a block are bounded from above by an integer m > 0, also known as m-gap-bounded partitions. This problem is harder than known…

### Actions and Identities on Set Partitions

- MathematicsElectron. J. Comb.
- 2012

A group action of A n on the set of A-labeled partitions of an (n + 1)-set is derived and new combinatorial proofs of Coker’s identity for the Narayana polynomial and its type B analogue are derived.

### Identities Derived from Noncrossing Partitions of Type B

- MathematicsElectron. J. Comb.
- 2011

Based on weighted noncrossing partitions of type $B$, we obtain type $B$ analogues of Coker's identities on the Narayana polynomials. A parity reversing involution is given for the alternating sum of…

### d-REGULAR SET PARTITIONS AND ROOK PLACEMENTS

- Mathematics
- 2009

We use a classical correspondence between set partitions and rook place- ments on the triangular board to give a quick picture understanding of the "reduction identity" |P (d) (n, k)| = |P (d j) (n −…

### Weighted 2-Motzkin Paths

- Mathematics
- 2004

This paper is motivated by two problems recently proposed by Coker on combinatorial identities related to the Narayana polynomials and the Catalan numbers. We find that a bijection of Chen, Deutsch…

### Fubini Numbers and Polynomials of Graphs

- MathematicsMediterranean Journal of Mathematics
- 2021

In this paper, we introduce the Fubini number and Fubini polynomial of a graph in connection with the enumeration of ordered independent partitions of its set of vertices. We prove several properties…

### Matchings Avoiding Partial Patterns

- MathematicsElectron. J. Comb.
- 2006

In the sense of Wilf-equivalence, the method of generating trees is used to show that the patterns 12132, 12123, 12321, 12231, 12213 are all equivalent to the pattern $12312$.

## References

SHOWING 1-10 OF 19 REFERENCES

### On abab-free and abba-free Set Partitions

- MathematicsEur. J. Comb.
- 1996

This work summarizes and extends known enumeriative results for the patternp=ababand to give an explicit formula for the number of p(abab, n, l, k) of partitions of such partitions.

### On the structure of the lattice of noncrossing partitions

- MathematicsDiscret. Math.
- 1991

### A map-theoretic approach to Davenport-Schinzel sequences.

- Mathematics
- 1972

An (n, d) Davenport-Schinzel Sequence (more briefly, a DS sequence) is a sequence of symbols selected from 1,2, , n, with the properties that (1) no two adjacent symbols are identical, (2) no…

### A bijection between ordered trees and 2-Motzkin paths and its many consequences

- MathematicsDiscret. Math.
- 2002

### A Construction for Enumerating k-coloured Motzkin Paths

- MathematicsCOCOON
- 1995

A method for enumerating k- coloured Motzkin paths according to various parameters is illustrated and a recursive description of these paths is given from which it is deduced the k- colored MotZkin paths' generating function according to their length, area and last fall length.

### Combinatorics of RNA Secondary Structures

- MathematicsDiscret. Appl. Math.
- 1998