Modernising Integer Partitions: Implementing Standard Iterators for the partitions Package
Sam Kamperis 
Robin Hankin
Executive Summary
Overview
The partitions package (Robin K. S. Hankin 2006) is widely used R infrastructure, but its current APIs either materialise all partitions in memory or require non-standard manual iteration. This proposal will add a standard S3 iterator interface (Analytics and Weston 2022), enabling lazy evaluation, lower memory use, and direct interoperability with tools such as foreach and itertools (Weston and Wickham 2014). The work is low-risk and high-leverage because it modernises the interface layer while preserving the package’s established enumeration logic.
Project Scope
Primary deliverable: an S3 partitions_iter class conforming to the iterators interface.
Secondary deliverables: documentation, worked examples, interoperability tests, and CRAN-ready release preparation.
Budget & Timeline
We request $8,374.74 to fund 124 hours of development over six months (July-December 2026), jointly delivered by Oxford Brookes University and the University of Stirling.
Team
The project is led by the grant applicant (9.7% FTE over 6 months) with Robin Hankin, the original partitions package author, as a collaborator providing technical guidance, code review, and CRAN liaison.
Expected Impact
This modernisation will make partitions usable in contemporary iterator and parallel workflows for its 1.3 million-download user base, reducing memory risk and replacing bespoke iteration code with standard, composable workflows.
Signatories
Project team
Sam Kamperis and Robin Hankin will deliver the project. Hankin is the original author of partitions and will provide technical review and release guidance.
Consulted
Feedback was sought from James Maunder, Fridolin Wild, and Inna Skarga-Bandurova.
The Problem
What Is the Problem?
The partitions package (Robin K. S. Hankin 2006) currently offers either bulk-generation functions (parts(), restrictedparts(), diffparts()) that materialise all results in memory, or low-level stepwise functions (firstpart()/nextpart()) that require manual state management. This is increasingly misaligned with modern R workflows. Partition counts grow explosively, so even moderate inputs can become impractical with bulk generation: for example, \(p(50) = 204,226\) and \(p(100)\) is approximately 190 million. At the same time, the manual stepping API does not implement the standard iterators interface (Analytics and Weston 2022), so users cannot use partition streams directly in foreach, itertools (Weston and Wickham 2014), or related parallel tooling without custom wrappers.
Who Is Affected?
With 1.3 million total downloads and 6,000–8,000 monthly users, the package affects researchers, statisticians, operations researchers, and practitioners who need scalable combinatorial workflows.
Why Is This a Problem?
- Ecosystem misalignment: standard R tooling (
foreach,itertools,furrr(Vaughan and Dancho 2022)) expectsnextElem-style iterators. - Memory constraints: practical inputs are unsafe with full matrix materialisation.
- Concurrency barriers: non-standard iteration blocks straightforward parallel and distributed use.
What Will Solving This Enable?
Implementing standard iterators will enable lazy evaluation, unlock parallel workflows, improve interoperability with iterator combinators, and let users write familiar R code instead of bespoke control loops.
Existing Work & Precedent
Standard iterator support is already established in the R ecosystem. This project brings partitions into that convention while preserving the existing firstpart()/nextpart() API for backward compatibility.
Competitive Landscape
Related packages such as RcppAlgos (Wood 2026b, 2026a) and arrangements (Lai 2020) provide strong combinatorial tooling, but use package-specific iteration interfaces. Our approach is complementary: we modernise the partitions interface layer so its unique partition semantics integrate directly with standard iterator tooling rather than through bespoke adapters.
The Proposal
Overview
We will modernise the partitions package (Robin K. S. Hankin 2006) by implementing the standard S3 iterators protocol (Analytics and Weston 2022). The core deliverable is a new partitions_iter S3 class with nextElem, allowing partition enumerations to be used directly in foreach() loops, itertools (Weston and Wickham 2014) pipelines, and parallel workflows. The solution preserves existing APIs and wraps the current stepping logic rather than replacing it, which keeps the implementation low-risk and compatible with existing users.
Delivery
The minimum viable implementation includes a partitions_iter class, nextElem.partitions_iter(), and factory functions iparts(), irestrictedparts(), and idiffparts(), together with testthat (Wickham 2011) coverage demonstrating equivalence with bulk-generation outputs and independent iterator coexistence. We will benchmark bulk versus lazy memory behaviour and confirm interoperability with foreach and itertools. Detailed architecture, benchmark protocols, and risk controls are provided in the companion plan (Project Plan).
Evidence of Impact
With ~1.3 million cumulative downloads and 6,000–8,000 monthly downloads, the package is a foundational tool in the R ecosystem. This level of usage, comparable to well-established data manipulation and statistical packages, justifies investment in modernising its infrastructure to integrate with contemporary R practices (lazy evaluation, functional programming, parallelisation).
Users across combinatorics research, statistics, operations research, and scientific computing depend on this package. Enabling standard iterator support will unlock new use cases and remove artificial barriers to productivity for researchers working with large combinatorial spaces.
Project Plan
Delivery is structured across six phases over six months (July-December 2026). The main proposal reports milestones and outcomes at a high level; full operational detail appears in Project Plan.
| Phase | Duration | Key Deliverables | Effort |
|---|---|---|---|
| Start-up | July | Collaboration setup, scope finalisation, CI baseline | 16 hrs |
| Core implementation | August | iparts(), irestrictedparts(), idiffparts(), nextElem methods, core tests |
24 hrs |
| Integration and testing | September | foreach and itertools integration, expanded tests |
20 hrs |
| Vignette and documentation | October | Quarto vignette, examples, README and docs updates | 32 hrs |
| Review and release | November | Final review, issue triage, CRAN submission preparation | 20 hrs |
| Publicity and dissemination | December | CRAN follow-up and public communication | 12 hrs |
| Total | July-December 2026 | Modernised iterator interface and release | 124 hrs |
Budget Summary
- Total funding requested: $8,374.74
- Total duration: 6 months
- Total effort: 124 hours (Sam Kamperis: 80; Robin Hankin: 44)
Availability and Dissemination
All outputs remain under the package’s GPL-3 licence. Development and review will be conducted via the official GitHub repository with transparent issue and pull-request tracking. Dissemination includes project updates during delivery and a post-release technical communication to the R community.
Success
Definition of Done
Success is defined by five outcomes: code merged and released to CRAN; partitions_iter compliant with the iterators S3 interface; tested correctness and interoperability; user documentation with worked examples; and iterator-related issues resolved or explicitly triaged.
Measuring Success
We will track the following headline metrics throughout the project:
| Metric | Success Criterion | Measurement Method |
|---|---|---|
| Coverage | >= 90% of new iterator code tested | covr report |
| Checks | devtools::check() and R CMD check pass cleanly |
CI and CRAN dry-run |
| Interop | foreach() and itertools examples run without error |
Tests and vignette examples |
| Memory | Peak memory of lazy iteration is <= 10% of equivalent bulk generation for large n | Benchmark scripts |
For implementation-level architecture, benchmark protocols, detailed monthly milestones, and expanded risk management, see the standalone companion document Project Plan.