A Linear Representation for Constant Term Sequences mod $p^a$ with Applications to Uniform Recurrence
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909555868303360 |
|---|---|
| author | Kohen, Nadav |
| author_facet | Kohen, Nadav |
| contents | Many integer sequences including the Catalan numbers, Motzkin numbers, and the Apr{é}y numbers can be expressed in the form ConstantTermOf$\left[P^nQ\right]$ for Laurent polynomials $P$ and $Q$. These are often called ``constant term sequences''. In this paper, we characterize the prime powers, $p^a$, for which sequences of this form modulo $p^a$, and others built out of these sequences, are uniformly recurrent. For all other prime powers, we show that the frequency of $0$ is $1$. This is accomplished by introducing a novel linear representation of constant term sequences modulo $p^a$, which is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Linear Representation for Constant Term Sequences mod $p^a$ with Applications to Uniform Recurrence Kohen, Nadav Combinatorics Representation Theory 11B50 (Primary) 68R15, 11B85 (Secondary) Many integer sequences including the Catalan numbers, Motzkin numbers, and the Apr{é}y numbers can be expressed in the form ConstantTermOf$\left[P^nQ\right]$ for Laurent polynomials $P$ and $Q$. These are often called ``constant term sequences''. In this paper, we characterize the prime powers, $p^a$, for which sequences of this form modulo $p^a$, and others built out of these sequences, are uniformly recurrent. For all other prime powers, we show that the frequency of $0$ is $1$. This is accomplished by introducing a novel linear representation of constant term sequences modulo $p^a$, which is of independent interest. |
| title | A Linear Representation for Constant Term Sequences mod $p^a$ with Applications to Uniform Recurrence |
| topic | Combinatorics Representation Theory 11B50 (Primary) 68R15, 11B85 (Secondary) |
| url | https://arxiv.org/abs/2503.21988 |