Algorithm for Calculating the Number of Derivations on Chain Lattice

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Published: Dec 27, 2022
Keywords:
Derivation Lattice Chain Lattice

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Paichayon Sirisatianwattana
Program of Mathematics, Faculty of Science and Technology, Kamphaeng Phet Rajabhat University
Charuntorn Kongin
Faculty of Science and Technology, Kamphaeng Phet Rajabhat University

Abstract

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


gif.latex?\left&space;|&space;d\left&space;(&space;Ch_{n}&space;\right&space;)&space;\right&space;|=&space;2^{n-1}


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:


gif.latex?\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 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 https://li01.tci-thaijo.org/index.php/jstcrru/article/view/256177
Issue
Vol. 1 No. 2 (2022): July - December
Section
Research article
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References

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