Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.20521 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914054287654912 |
|---|---|
| author | Hopkins, Brian Munagi, Augustine |
| author_facet | Hopkins, Brian Munagi, Augustine |
| contents | Integer compositions restricted by inequalities on certain pairs of parts were first considered by Jörg Arndt in 2013 and several variations have been studied recently. Here we consider a broad two-parameter generalization that scales the defining relation. We connect these to compositions restricted to parts from certain congruence classes and establish the recurrence relations satisfied by the related counting sequences. This provides new combinatorial interpretations to several documented integer sequences and also simple unrecorded sequences. We conclude with suggestions for further study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaled Arndt Compositions Hopkins, Brian Munagi, Augustine Combinatorics 05A17, 11B37 Integer compositions restricted by inequalities on certain pairs of parts were first considered by Jörg Arndt in 2013 and several variations have been studied recently. Here we consider a broad two-parameter generalization that scales the defining relation. We connect these to compositions restricted to parts from certain congruence classes and establish the recurrence relations satisfied by the related counting sequences. This provides new combinatorial interpretations to several documented integer sequences and also simple unrecorded sequences. We conclude with suggestions for further study. |
| title | Scaled Arndt Compositions |
| topic | Combinatorics 05A17, 11B37 |
| url | https://arxiv.org/abs/2509.20521 |