Pitiwat Lueangwitchajaroen

Pitiwat Lueangwitchajaroen

A self-taught learner who is fascinated in Math🧮, Neuroscience🧠, and Computer Vision👾.

Publications

The Formula of the Frobenius Number for a Numerical Semigroup with Embedding Dimension Three respect to a Partial Order Relation

Published in Asian Health, Science and Technology Reports (formerly NUJST), 2023

The Frobenius number is the largest positive integer that cannot be expressed as a non-negative linear combination of a given set of positive integers. It is considered to be one of the well-known problems in number theory, especially where the cardinality of the set is greater than three. Recently, algorithms and formulas have been proposed to calculate the Frobenius number in three variables, and various techniques have been used to handle the problem. Currently, for more than three variables, the problem associated with finding the Frobenius number is still considered to be an open problem. In this work, we used the concept of a numerical semigroup to develop an alternative approach to finding the Frobenius and genus number in three variables in particular cases. In the arbitrary variables, the formula presented in three variables can yield an upper bound of the Frobenius number and genus number.

Recommended citation: Lueangwitchajaroen, P., Laysirikul, E., The Formula of the Frobenius Number for a Numerical Semigroup with Embedding Dimension Three respect to a Partial Order Relation, NUJST: Science and Technology, 31 (2) (2023) 33 - 41. https://ph03.tci-thaijo.org/index.php/ahstr/article/view/1056

Affine Rational Transformations of Copulas and Quasi-Copulas

Published in Thai Journal of Mathematics, 2022

The transformation-based methods are indeed the convenient ways for constructing a newcopula using known copulas. In this research, we characterize linear rational transformations for mul-tivariate copulas and multivariate quasi-copulas. This is an extension to the already known results inthe bivariate case. We found that this type of transformations extended naturally for the multivariatequasi-copulas. Yet, the only linear rational transformation of multivariate copulas is the identity functionwhich is different from the bivariate case. This means that the set of linear rational functions that trans-form a multivariate copula varies depending on the copula itself. As an example, we also characterizesuch sets in the case of the trivariate product copula.

Recommended citation: Lueangwitchajaroen, P., Tasena, S., Affine Rational Transformations of Copulas and Quasi-Copulas, Thai Journal of Mathematics, 20 (4) (2022) 1649 - 1660. https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1428