Algorithm for Calculating the Number of Derivations on Chain Lattice

Abstract

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

$\left&space;|&space;d\left&space;(&space;Ch_{n}&space;\right&space;)&space;\right&space;|=&space;2^{n-1}$

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

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

$\left&space;|&space;d\left&space;(&space;Ch_{n}&space;\right&space;)&space;\right&space;|=&space;2^{n-1}=&space;\Sigma&space;_{k=0}^{n-1}\binom{n-1}{k}=&space;F_{n+1'}^{(n)}$

where $F_{n+1}^{(n)}$ is the ($n+1$)-th Fibonacci $n-Step$  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 https://li01.tci-thaijo.org/index.php/jstcrru/article/view/256177
Section
Research article

References

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