A new diagrammatic 2-category models induction and restriction on Temperley-Lieb modules, with a basis theorem implying an equivalence after Karoubi completion and a positive basis from homogenized Chebyshev polynomials.
Linear transformation distance for bichromatic matchings
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Let $P=B\cup R$ be a set of $2n$ points in general position, where $B$ is a set of $n$ blue points and $R$ a set of $n$ red points. A \emph{$BR$-matching} is a plane geometric perfect matching on $P$ such that each edge has one red endpoint and one blue endpoint. Two $BR$-matchings are compatible if their union is also plane. The \emph{transformation graph of $BR$-matchings} contains one node for each $BR$-matching and an edge joining two such nodes if and only if the corresponding two $BR$-matchings are compatible. In SoCG 2013 it has been shown by Aloupis, Barba, Langerman, and Souvaine that this transformation graph is always connected, but its diameter remained an open question. In this paper we provide an alternative proof for the connectivity of the transformation graph and prove an upper bound of $2n$ for its diameter, which is asymptotically tight.
fields
math.RT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
A Graphical Calculus for Induction and Restriction on Temperley-Lieb Modules
A new diagrammatic 2-category models induction and restriction on Temperley-Lieb modules, with a basis theorem implying an equivalence after Karoubi completion and a positive basis from homogenized Chebyshev polynomials.