A semigroup approach to iterated binomial transforms
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915749310758912 |
|---|---|
| author | Verwee, Johann |
| author_facet | Verwee, Johann |
| contents | We study a one-parameter family of binomial-convolution operators acting on sequences. These operators form an additive semigroup with an explicit inverse, and they subsume iterated classical binomial transforms as a special case. We describe the action in terms of ordinary and exponential generating functions, interpret the transform in the Riordan-array framework, and prove a general root-shift principle for constant-coefficient linear recurrences: applying the transform shifts the characteristic roots by a fixed amount. Several classical families (Fibonacci, Lucas, Pell, Jacobsthal, Mersenne) are treated uniformly as illustrative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12579 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A semigroup approach to iterated binomial transforms Verwee, Johann Combinatorics 05A19 (Primary) 11B37 (Secondary) We study a one-parameter family of binomial-convolution operators acting on sequences. These operators form an additive semigroup with an explicit inverse, and they subsume iterated classical binomial transforms as a special case. We describe the action in terms of ordinary and exponential generating functions, interpret the transform in the Riordan-array framework, and prove a general root-shift principle for constant-coefficient linear recurrences: applying the transform shifts the characteristic roots by a fixed amount. Several classical families (Fibonacci, Lucas, Pell, Jacobsthal, Mersenne) are treated uniformly as illustrative examples. |
| title | A semigroup approach to iterated binomial transforms |
| topic | Combinatorics 05A19 (Primary) 11B37 (Secondary) |
| url | https://arxiv.org/abs/2601.12579 |