## 191 Citations

### Some identities on the Catalan, Motzkin and Schröder numbers

- MathematicsDiscret. Appl. Math.
- 2008

### Motzkin numbers revisited

- Mathematics
- 2018

Motzkin numbers, like Catalan numbers, have important role in number theory and they preserve their own identity in many ways. In this note we have, as mentioned in the title, have revisited the…

### Identities involving weighted Catalan, Schröder and Motzkin paths

- MathematicsAdv. Appl. Math.
- 2017

### Combinatorics of Generalized Motzkin Numbers

- MathematicsJ. Integer Seq.
- 2015

The generalized Motzkin numbers are common generalizations of the MotZkin numbers and the Catalan numbers investigated, including the combinatorial interpretation, the recurrence relation, the binomial Transform, the Hankel transform, the log-convexity, the continued fraction of the generating function, and the total positivity of the corresponding Hankel matrix.

### Catalan Numbers Modulo 2 k

- Mathematics
- 2010

In this paper, we develop a systematic tool to calculate the congruences of some combinatorial numbers involving n!. Using this tool, we re-prove Kummer’s and Lucas’ theorems in a unique concept, and…

### Walking in the OEIS: From Motzkin numbers to Fibonacci numbers. The "shadows" of Motzkin numbers

- Mathematics
- 2021

In this paper, we consider nine OEIS sequences, the analysis of which allows us to find a connection between Motzkin numbers and Fibonacci numbers. In each Motzkin number, we distinguish an even…

### Semiorders and Riordan Numbers

- Mathematics
- 2007

In this paper, we define a class of semiorders (or unit interval orders) that arose in the context of polyhedral combinatorics. In the first section of the paper, we will present a pure counting…

## References

SHOWING 1-10 OF 18 REFERENCES

### Restricted plane tree representations of four Motzkin-Catalan equations

- MathematicsJ. Comb. Theory, Ser. B
- 1977

### Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products

- Mathematics
- 1948

This note improves, in two respects, the results of §3.6 of my paper The hyper surface cross ratio. There it is shown that the number cn of independent hypersurface cross ratios that can be formed of…

### Historical Note on a Recurrent Combinatorial Problem

- Mathematics
- 1965

ISSN: 0002-9890 (Print) 1930-0972 (Online) Journal homepage: https://www.tandfonline.com/loi/uamm20 Historical Note on a Recurrent Combinatorial Problem William G. Brown To cite this article: William…

### MORSELT, A note on plane trees

- J. Combinatorial Theory
- 1967