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- Title
Partitions associated to class groups of imaginary quadratic number fields.
- Authors
Petersen, Kathleen L.; Sellers, James A.
- Abstract
We investigate properties of attainable partitions of integers, where a partition (n 1 , n 2 , ⋯ , n r) of n is attainable if ∑ (3 - 2 i) n i ≥ 0 . Conjecturally, under an extension of the Cohen and Lenstra heuristics by Holmin et. al., these partitions correspond to abelian p-groups that appear as class groups of imaginary quadratic number fields for infinitely many odd primes p. We demonstrate a connection to partitions of integers into triangular numbers, construct a generating function for attainable partitions, and determine the maximal length of attainable partitions.
- Subjects
PARTITION functions; QUADRATIC fields; GENERATING functions; INTEGERS; PARTITIONS (Mathematics)
- Publication
Aequationes Mathematicae, 2023, Vol 97, Issue 1, p63
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-022-00899-x