Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
The number of smallest parts of Partitions of n
View through CrossRef
George E Andrews derived formula for the number of smallest parts of partitions of a positive integer n. In this paper we derived the generating function for the number of smallest parts of all partitions of n utilizing r-partitions of n. We also derive the generating function for Ac(n) , the number of smallest parts of the partitions of n which are multiples of c and also to evaluate the sum of smallest parts of partitions of n by applying the concept of r-partitions of n.
Title: The number of smallest parts of Partitions of n
Description:
George E Andrews derived formula for the number of smallest parts of partitions of a positive integer n.
In this paper we derived the generating function for the number of smallest parts of all partitions of n utilizing r-partitions of n.
We also derive the generating function for Ac(n) , the number of smallest parts of the partitions of n which are multiples of c and also to evaluate the sum of smallest parts of partitions of n by applying the concept of r-partitions of n.
Related Results
Quelques résultats combinatoires autour de la décomposition de Littlewood
Quelques résultats combinatoires autour de la décomposition de Littlewood
Cette thèse s'intéresse à des objets de combinatoire énumérative et plus particulièrement aux partitions d'entiers. Les partitions et les tableaux de Young sont des objets combinat...
Partition Diversity in Complex Networks
Partition Diversity in Complex Networks
Diversité des partitions dans les réseaux complexes
La diversité des partitions dans les réseaux complexes provient de la coexistence de multiples manières plausibl...
Some New Results on the Number of Tagged Parts Over the Partitions with Designated Summands
Some New Results on the Number of Tagged Parts Over the Partitions with Designated Summands
The partitions with designated summands were introduced. In such partitions, among those parts of the same magnitude, one is tagged or designated. This work presents some new resul...
A Comparison of Integer Partitions Based on Smallest Part
A Comparison of Integer Partitions Based on Smallest Part
For positive integers $n, L$ and $s$, consider the following two sets that both contain partitions of $n$ with the difference between the largest and smallest parts bounded by $L$:...
Congruences for hook lengths of partitions
Congruences for hook lengths of partitions
Recently, Amdeberhan
et al.
[Proc. Amer. Math. Soc. Ser. B 11 (2024), pp. 345–357] proved congruences for the number of hooks of fixed even ...
Hyperarbres et Partitions semi-pointées : aspects combinatoires, algébriques et homologiques
Hyperarbres et Partitions semi-pointées : aspects combinatoires, algébriques et homologiques
Cette thèse est consacrée à l’étude combinatoire, algébrique et homologique des hyperarbres et des partitions semi-pointées. Nous étudions plus précisément des structures algébriqu...
CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION
CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION
A well-known problem regarding the integer partition function p(n) is the parity problem, how often is p(n) even or odd? Motivated by this problem, we obtain the following results:...
Developing a Quality Flag for the SAR Ocean Wave Spectrum Partitioning with Machine Learning
Developing a Quality Flag for the SAR Ocean Wave Spectrum Partitioning with Machine Learning
Synthetic aperture radar (SAR) is one of the few instruments capable of providing high-resolution global two-dimensional (2D) measurements of ocean waves. Since 2014 and then 2016,...