Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 43 min ago
Peer-reviewedCC BY 4.0Axioms

Balanced Notation for τ-Rigid Pairs

  • Kiyoshi Igusa1
  • Gordana Todorov2
  1. 1Mathematics Department, Brandeis University, Waltham, MA 02453, USA
  2. 2Department of Mathematics, Northeastern University, Boston, MA 02115, USA
Open at sourceDOICite

Abstract

We introduce a new notation for τ-rigid pairs called “balanced pairs”. The notation AB allows for simplification of some formulas, for example, the Jasso category and its dual. One of the most compelling formulas is that in the hereditary case, the bricks that label the “covering” and “flooring” walls for the g-vector of AB are precisely A and B respectively. In the general case, we give a precise formula for these wall labels. We also define “lower” and “upper” chambers for g(AB), and we prove that these correspond to generalized Bongartz and co-Bongartz completions of the balanced pair AB.

Related

  1. Ideal balanced pairs in n-exangulated categories
    Peiyu Zhang, Zhuolin Zheng, Li Wang +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Gorenstein cotorsion pairs induced by balanced pairs
    Konstantinos Golfis
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. SNACK: A Sequential Notation Framework for Probabilistic Graph Generation
    Hohyun Kim, Hyesung Kim, Min-hwan Oh +1
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  4. A compact notation for peculiar properties characterizing integer tetration
    Marco Ripà, Gabriele Di Pietro
    Notes on Number Theory and Discrete MathematicsPeer-reviewedCC BYFull text8 citedMathematical physicsOpenAlex
  5. Rigid dualizing complex for quantum enveloping algebras and algebras of generalized differential operators
    Sophie Chemla
    Journal of AlgebraPeer-reviewedLicence not stated25 citedGeometry & topologyHAL

Cite

BibTeXRIS
BibTeX
@article{igusa2026balanced,
  title = {{Balanced Notation for τ-Rigid Pairs}},
  author = {Kiyoshi Igusa and Gordana Todorov},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100731},
  url = {https://www.mdpi.com/2075-1680/15/10/731},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Balanced Notation for τ-Rigid Pairs
AU  - Kiyoshi Igusa
AU  - Gordana Todorov
PY  - 2026
DA  - 2026/10/01
JO  - Axioms
DO  - 10.3390/axioms15100731
UR  - https://www.mdpi.com/2075-1680/15/10/731
AB  - We introduce a new notation for τ-rigid pairs called “balanced pairs”. The notation AB allows for simplification of some formulas, for example, the Jasso category and its dual. One of the most compelling formulas is that in the hereditary case, the bricks that label the “covering” and “flooring” walls for the g-vector of AB are precisely A and B respectively. In the general case, we give a precise formula for these wall labels. We also define “lower” and “upper” chambers for g(AB), and we prove that these correspond to generalized Bongartz and co-Bongartz completions of the balanced pair AB.
SN  - 2075-1680
ER  -