{"title":"Coxeter Invariants for Non-negative Unit Forms of Dynkin Type 𝔸r","authors":"Jesús Arturo Jiménez González","doi":"10.3233/fi-222109","DOIUrl":null,"url":null,"abstract":"Two integral quadratic unit forms are called strongly Gram congruent if their upper triangular Gram matrices are ℤ-congruent. The paper gives a combinatorial strong Gram invariant for those unit forms that are non-negative of Dynkin type 𝔸r (for r ≥ 1), within the framework introduced in [Fundamenta Informaticae 184(1):49–82, 2021], and uses it to determine all corresponding Coxeter polynomials and (reduced) Coxeter numbers.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Informaticae","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.3233/fi-222109","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 5
Abstract
Two integral quadratic unit forms are called strongly Gram congruent if their upper triangular Gram matrices are ℤ-congruent. The paper gives a combinatorial strong Gram invariant for those unit forms that are non-negative of Dynkin type 𝔸r (for r ≥ 1), within the framework introduced in [Fundamenta Informaticae 184(1):49–82, 2021], and uses it to determine all corresponding Coxeter polynomials and (reduced) Coxeter numbers.
期刊介绍：
Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
solutions by mathematical methods of problems emerging in computer science
solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to):
theory of computing,
complexity theory,
algorithms and data structures,
computational aspects of combinatorics and graph theory,
programming language theory,
theoretical aspects of programming languages,
computer-aided verification,
computer science logic,
database theory,
logic programming,
automated deduction,
formal languages and automata theory,
concurrency and distributed computing,
cryptography and security,
theoretical issues in artificial intelligence,
machine learning,
pattern recognition,
algorithmic game theory,
bioinformatics and computational biology,
quantum computing,
probabilistic methods,
algebraic and categorical methods.
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