Injectivity of polynomials over finite discrete dynamical systems

[2502.02360] Injectivity of polynomials over finite discrete dynamical systems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Discrete Mathematics arXiv:2502.02360 (cs) [Submitted on 4 Feb 2025] Title: Injectivity of polynomials over finite discrete dynamical systems Authors: Antonio E. Porreca , Marius Rolland View a PDF of the paper titled Injectivity of polynomials over finite discrete dynamical systems, by Antonio E. Porreca and Marius Rolland View PDF HTML (experimental) Abstract: The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering. The decomposition of dynamics into simpler subsystems allows us to simplify this analysis (or design). Here we focus on an algebraic approach to decomposition, based on alternative and synchronous execution as the sum and product operations; this gives rise to polynomial equations (with a constant side). In this article we focus on univariate, injective polynomials, giving a characterization in terms of the form of their coefficients and a polynomial-time algorithm for solving the associated equations. Subjects: Discrete Mathematics (cs.DM) ; Dynamical Systems (math.DS) Cite as: arXiv:2502.02360 [cs.DM] (or arXiv:2502.02360v1 [cs.DM] for this version) https://doi.org/10.48550/arXiv.2502.02360 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/978-3-031-95908-0_27 Focus to learn more DOI(s) linking to related resources Submission history From: Marius Rolland [ view email ] [v1] Tue, 4 Feb 2025 14:44:25 UTC (228 KB) Full-text links: Access Paper: View a PDF of the paper titled Injectivity of polynomials over finite discrete dynamical systems, by Antonio E. Porreca and Marius Rolland View PDF HTML (experimental) TeX Source view license Current browse context: cs.DM < prev | next > new | recent | 2025-02 Change to browse by: cs math math.DS References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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