A polynomial time algorithm for almost bounded denumerant

[2608.14985] A polynomial time algorithm for almost bounded denumerant Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2608.14985 (math) [Submitted on 15 Aug 2026] Title: A polynomial time algorithm for almost bounded denumerant Authors: Guoce Xin , Chen Zhang , Zihao Zhang View a PDF of the paper titled A polynomial time algorithm for almost bounded denumerant, by Guoce Xin and 2 other authors View PDF HTML (experimental) Abstract: Sylvester's denumerant $d(t; \boldsymbol{A})$ counts the number of nonnegative integer solutions to $\sum_{i=1}^{N} a_i x_i = t$, where $\boldsymbol{A} = (a_1, \dots, a_N)$ is a sequence of positive integers with $\gcd(\boldsymbol{A}) = 1$. In 2025, Xin and Zhang gave a polynomial time algorithm in $N$ for computing $d(t; \boldsymbol{A})$ when the entries of $\boldsymbol{A}$ are bounded by a constant. In this paper, we extend this algorithm by incorporating Barvinok's algorithm, enabling it to handle the case where a fixed number of entries of $\boldsymbol{A}$ are allowed to be unbounded. Comments: 12 pages Subjects: Combinatorics (math.CO) MSC classes: Primary 05A17, Secondary 11P81, 05--08 Cite as: arXiv:2608.14985 [math.CO] (or arXiv:2608.14985v1 [math.CO] for this version) https://doi.org/10.48550/arXiv.2608.14985 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Chen Zhang [ view email ] [v1] Sat, 15 Aug 2026 02:26:25 UTC (12 KB) Full-text links: Access Paper: View a PDF of the paper titled A polynomial time algorithm for almost bounded denumerant, by Guoce Xin and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2026-08 Change to browse by: math 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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