Algorithm for Calculating the Number of Derivations on Chain Lattice

Main Article Content

Paichayon Sirisatianwattana
Charuntorn Kongin


This paper presents the formula for finding the number of derivations on chain lattice with gif.latex?n elements. The formula is,


where gif.latex?n is a positive integer, gif.latex?Ch_{n}  denoted a chain lattice with gif.latex?n elements and gif.latex?\left&space;|&space;d\left&space;(&space;Ch_{n}&space;\right&space;)&space;\right&space;| is all the numbers of derivations of chain lattices.

Moreover, we found that the number of derivations of gif.latex?Ch_{n} can be computed in binomial coefficient form and related to some of Fibonacci numbers as follows:


where gif.latex?F_{n+1}^{(n)} is the (gif.latex?n+1)-th Fibonacci gif.latex?n-Step  number.

Article Details

How to Cite
Sirisatianwattana, P., & Kongin, C. (2022). Algorithm for Calculating the Number of Derivations on Chain Lattice. Journal of Science and Technology CRRU, 1(2), 27–37. Retrieved from
Research article


Davey, B. A., & Priestley, H. A. (2002). Introduction to lattices and order (2nd ed.) New York: Cambridge University Press.

Jokar, Z., Hosseini, A., & Niknam, A. (2016). Some conditions under which Jordan derivations are zero. Iran: Ferdowsi University of Mashhad.

Mayuka, F. K., & Michiro, K. (2016). Note on derivations of lattices. Japan: Hokkaido University.

Ferrari, L. (2001). On derivations of lattices. Italy: Firenze.

Xin, X. L., Li, T. Y., & Lu, J. H. (2007). On derivations of lattices. China: China College of Science.