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Peer-reviewedCC BY 4.0The Electronic Journal of Combinatorics

Noncrossing Arc Diagrams of Type B

  • Emily Barnard
  • Nathan Reading
  • Ashley Tharp
Open at sourcePDFDOICite

Abstract

Noncrossing arc diagrams are combinatorial models for permutations that encode information about lattice congruences of the weak order and about the associated discrete geometry. In this paper, we consider two related, analogous models for signed permutations. One model features centrally symmetric noncrossing arc diagrams, while the other features their quotients modulo the central symmetry. We demonstrate the utility of the models by applying them to various questions about lattice quotients of the weak order.

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Cite

BibTeXRIS
BibTeX
@article{barnard2026noncrossing,
  title = {{Noncrossing Arc Diagrams of Type B}},
  author = {Emily Barnard and Nathan Reading and Ashley Tharp},
  journal = {The Electronic Journal of Combinatorics},
  year = {2026},
  month = nov,
  doi = {10.37236/14125},
  url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p35},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Noncrossing Arc Diagrams of Type B
AU  - Emily Barnard
AU  - Nathan Reading
AU  - Ashley Tharp
PY  - 2026
DA  - 2026/11/06
JO  - The Electronic Journal of Combinatorics
DO  - 10.37236/14125
UR  - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p35
AB  - Noncrossing arc diagrams are combinatorial models for permutations that encode information about lattice congruences of the weak order and about the associated discrete geometry. In this paper, we consider two related, analogous models for signed permutations. One model features centrally symmetric noncrossing arc diagrams, while the other features their quotients modulo the central symmetry. We demonstrate the utility of the models by applying them to various questions about lattice quotients of the weak order.
SN  - 1077-8926
ER  -