Cardinality of Number Partitions

 

Title: Cardinality of Number Partitions
Author: Lukas Bulwahn (lukas /dot/ bulwahn /at/ gmail /dot/ com)
Submission date: 2016-01-14
Abstract: This entry provides a basic library for number partitions, defines the two-argument partition function through its recurrence relation and relates this partition function to the cardinality of number partitions. The main proof shows that the recursively-defined partition function with arguments n and k equals the cardinality of number partitions of n with exactly k parts. The combinatorial proof follows the proof sketch of Theorem 2.4.1 in Mazur's textbook `Combinatorics: A Guided Tour`. This entry can serve as starting point for various more intrinsic properties about number partitions, the partition function and related recurrence relations.
BibTeX:
@article{Card_Number_Partitions-AFP,
  author  = {Lukas Bulwahn},
  title   = {Cardinality of Number Partitions},
  journal = {Archive of Formal Proofs},
  month   = jan,
  year    = 2016,
  note    = {\url{http://isa-afp.org/entries/Card_Number_Partitions.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Used by: Bell_Numbers_Spivey, Euler_Partition, Twelvefold_Way