English

Coxeter invariants for non-negative unit forms of Dynkin type A

Combinatorics 2023-06-22 v6

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 A, 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.

Keywords

Cite

@article{arxiv.2010.09991,
  title  = {Coxeter invariants for non-negative unit forms of Dynkin type A},
  author = {Jesús Arturo Jiménez González},
  journal= {arXiv preprint arXiv:2010.09991},
  year   = {2023}
}

Comments

Integral quadratic form, Gram congruence, Dynkin type, Coxeter polynomial, edge-bipartite graph, quiver, incidence matrix, signed line graph

R2 v1 2026-06-23T19:28:29.837Z