Algebraic entropies of natural numbers with one or two prime factors

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2016, v.23 no.3, pp.205-221

https://doi.org/10.7468/jksmeb.2016.23.3.205

JEONG, SEUNGPIL (DEPARTMENT OF MATHEMATICS, GYEONGSANG NATIONAL UNIVERSITY)
KIM, KYONG HOON (DEPARTMENT OF MATHEMATICS, GYEONGSANG NATIONAL UNIVERSITY)
KIM, GWANGIL (DEPARTMENT OF MATHEMATICS, GYEONGSANG NATIONAL UNIVERSITY)

JEONG, SEUNGPIL, KIM, KYONG HOON, & KIM, GWANGIL. (2016). ALGEBRAIC ENTROPIES OF NATURAL NUMBERS WITH ONE OR TWO PRIME FACTORS. 한국수학교육학회지시리즈B:순수및응용수학, 23(3), 205-221, https://doi.org/10.7468/jksmeb.2016.23.3.205

복사

Abstract

We formulate the additive entropy of a natural number in terms of the additive partition function, and show that its multiplicative entropy is directly related to the multiplicative partition function. We give a practical formula for the multiplicative entropy of natural numbers with two prime factors. We use this formula to analyze the comparative density of additive and multiplicative entropy, prove that this density converges to zero as the number tends to infinity, and empirically observe this asymptotic behavior.

keywords: entropy, partition function, additive entropy, multiplicative entropy, relative comparison density

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논문 상세

Vol.23 No.3

ALGEBRAIC ENTROPIES OF NATURAL NUMBERS WITH ONE OR TWO PRIME FACTORS

Algebraic entropies of natural numbers with one or two prime factors

Abstract

한국수학교육학회지시리즈B:순수및응용수학