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COLOR PARTITIONS AND GANDHI'S RECURRENCE RELATION

J. D. Bulnes|T. Kim|J. Lopez-Bonilla|M. Alegri
장전수학회 (Jangjeon Mathematical Society)|2024.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27권 제2호|pp. 393-397|DOI 10.17777/pjms.2024.27.2.024

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참고문헌

키워드

Sum of divisors functionZ-transformColor partitionsRecurrence relationsCompositionsBell polynomials
주제분류수학

초록

We employ the Z-transform to solve a type of recurrence relation satisfied by pₖ(n), the number of k-colored partitions of n; the corresponding solution is in terms of the complete Bell polynomials and it is equivalent to a recent formula deduced by Alegri. Thus, pₖ(n) is a polynomial in k of degree n whose coefficients are determined by the compositions of n.

Abstract

We employ the Z-transform to solve a type of recurrence relation satisfied by pₖ(n), the number of k-colored partitions of n; the corresponding solution is in terms of the complete Bell polynomials and it is equivalent to a recent formula deduced by Alegri. Thus, pₖ(n) is a polynomial in k of degree n whose coefficients are determined by the compositions of n.

참고문헌 (30)

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