{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-recurrence-relations-of-multi-dimensional","title":"On Recurrence Relations of Multi-dimensional Sequences","arxiv_id":"2410.17208","date":"2024-10-22","proceeding":null,"authors":["Hamid Rahkooy"],"abstract":"In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured matrices and computing their kernels. The challenging problem is to reduce the size of the corresponding matrices. In this paper, we show how to convert the problem of computing recurrence relations of multi-dimensional sequences into computing the orthogonal of certain ideals as subvector spaces of the dual module of polynomials. We propose an algorithm using efficient dual module computation algorithms. We present a complexity bound for this algorithm, carry on experiments using Maple implementation, and discuss the cases when using this algorithm is much faster than the existing approaches.","url_abs":"https://arxiv.org/abs/2410.17208v1","url_pdf":"https://arxiv.org/pdf/2410.17208v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-recurrence-relations-of-multi-dimensional","repo_url":"https://github.com/rahkooy/dual-annihilator","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}