Work

Balanced Notation for τ-Rigid Pairs

Year: 2026

Type: article

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.

Source: Axioms

DOI: 10.3390/axioms15100731

Authors: Kiyoshi Igusa, Gordana Todorov

Institutions: Brandeis University, Northeastern University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Simons Foundation