ON THE PARTITION FUNCTION

J. D. Bulnes; T. Kim; J. López-Bonilla; S. Vidal-Beltrán

doi:10.17777/pjms2023.26.1.1

ON THE PARTITION FUNCTION

J. D. Bulnes, T. Kim, J. López-Bonilla, S. Vidal-Beltrán

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

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Resumen

In this paper, we exhibit short deductions of the Jha and Malenfant expressions for the partition function, and we show several connections between the Euler, divisor and partition functions via the partial Bell polynomials and Hessenberg determinants. Besides, we show that the Gandhi's recurrence relation for colour partitions implies the Osler-Hassen-Chandrupatla's expression for the divisor function.

Idioma original	Inglés
Páginas (desde-hasta)	1-9
Número de páginas	9
Publicación	Proceedings of the Jangjeon Mathematical Society
Volumen	26
N.º	1
DOI	https://doi.org/10.17777/pjms2023.26.1.1
Estado	Publicada - 2023

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abstract = "In this paper, we exhibit short deductions of the Jha and Malenfant expressions for the partition function, and we show several connections between the Euler, divisor and partition functions via the partial Bell polynomials and Hessenberg determinants. Besides, we show that the Gandhi's recurrence relation for colour partitions implies the Osler-Hassen-Chandrupatla's expression for the divisor function.",

keywords = "Bell polynomials, Colour partitions, Hessenberg determinant, Malenfant and Jha formulas, Partition function, Sum of divisors function, q-analysis",

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AU - Bulnes, J. D.

AU - Kim, T.

AU - López-Bonilla, J.

AU - Vidal-Beltrán, S.

PY - 2023

Y1 - 2023

N2 - In this paper, we exhibit short deductions of the Jha and Malenfant expressions for the partition function, and we show several connections between the Euler, divisor and partition functions via the partial Bell polynomials and Hessenberg determinants. Besides, we show that the Gandhi's recurrence relation for colour partitions implies the Osler-Hassen-Chandrupatla's expression for the divisor function.

AB - In this paper, we exhibit short deductions of the Jha and Malenfant expressions for the partition function, and we show several connections between the Euler, divisor and partition functions via the partial Bell polynomials and Hessenberg determinants. Besides, we show that the Gandhi's recurrence relation for colour partitions implies the Osler-Hassen-Chandrupatla's expression for the divisor function.

KW - Bell polynomials

KW - Colour partitions

KW - Hessenberg determinant

KW - Malenfant and Jha formulas

KW - Partition function

KW - Sum of divisors function

KW - q-analysis

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SN - 1598-7264

VL - 26

SP - 1

EP - 9

JO - Proceedings of the Jangjeon Mathematical Society

JF - Proceedings of the Jangjeon Mathematical Society

IS - 1

ER -

ON THE PARTITION FUNCTION

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