| Home |
| About |
| Submission |
| Updating Entries |
| Using Entries |
| Search |
| Statistics |
| Index |
| Download |
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 |
| Status: [skipped] | This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. |
|
Proof outline Proof document |
| Browse theories |
| Download this entry |
Older releases:
|