Double orthodontia formulas and Lascoux positivity

[2410.08038] Double orthodontia formulas and Lascoux positivity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2410.08038 (math) [Submitted on 10 Oct 2024 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Double orthodontia formulas and Lascoux positivity Authors: Linus Setiabrata , Avery St. Dizier View a PDF of the paper titled Double orthodontia formulas and Lascoux positivity, by Linus Setiabrata and Avery St. Dizier View PDF HTML (experimental) Abstract: We give a new formula for double Grothendieck polynomials based on Magyar's orthodontia algorithm for diagrams. Our formula implies a similar formula for double Schubert polynomials $\mathfrak S_w(\mathbf x;\mathbf y)$. We also prove a curious positivity result: for vexillary permutations $w\in S_n$, the polynomial $x_1^n\dots x_n^n \mathfrak S_w(x_n^{-1}, \dots, x_1^{-1}; 1,\dots,1)$ is a graded nonnegative sum of Lascoux polynomials. We conjecture that this positivity result holds for all $w\in S_n$. This conjecture would follow from a problem of independent interest regarding Lascoux positivity of certain products of Lascoux polynomials. Comments: 19 pages, 7 figures. v2: minor editorial changes Subjects: Combinatorics (math.CO) Cite as: arXiv:2410.08038 [math.CO] (or arXiv:2410.08038v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2410.08038 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Linus Setiabrata [ view email ] [v1] Thu, 10 Oct 2024 15:32:02 UTC (136 KB) [v2] Sat, 15 Aug 2026 02:38:34 UTC (172 KB) Full-text links: Access Paper: View a PDF of the paper titled Double orthodontia formulas and Lascoux positivity, by Linus Setiabrata and Avery St. Dizier View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2024-10 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

Related documents

• Evaluating Laser and Piezocision vs. Piezocision Alone on Root Resorption and Gingival Health During Tooth Retraction#842958
• Changes in Pulpal Blood Flow Between Conventional and Self-ligating Fixed Orthodontic Brackets During Leveling and Alignment Stage#876002
• Assessment of Piezoelectric Periodontal Surgery Effects on Orthodontic Treatment: a Prospective Pilot Study#802909
• Molar Incisor Hypomineralisation and Dental Anomalies#1127891
• OrthoPulse 2.0 and 2.1 Feasibility Evaluation#843006