Tianyuan Xu

collaborators

5 papers

cs.IT2026

Minimum distance and decoding of Coxeter codes

Alexander Barg, QÃ«ndrim R. Gashi, Tianyuan Xu

A binary Coxeter code associated with a finite Coxeter system $(W, S)$ is an $F_{2}$ -linear span of indicators of standard cosets of a fixed rank. Coxeter codes, introduced…

math.CO2026

Perfect matchings, Fano planes, and orthogonal bases of type $E_{8}$

R. M. Green, Tianyuan Xu

We use perfect matchings and labelled Fano planes to construct and study the $2025$ orthogonal bases of positive roots in the $E_{8}$ root system. The set of these bases forms a high…

math.CO2026

Generalized Rothe diagrams for orthogonal roots

R. M. Green, Tianyuan Xu

Let $U$ be a set of positive roots of type $A D E$ , and let $Ω_{U}$ be the set of all maximum-cardinality orthogonal subsets of $U$ . We associate a generalized Rothe diagram to each el…

math.CO2026

Branching rules of minuscule representations via a new partial order

R. M. Green, Tianyuan Xu

We introduce a new partial order on the set of all antichains of a fixed size in any poset. When applied to minuscule posets, these partial orders give rise to distributive lattice…

math.CO2025

Orthogonal roots, Macdonald representations, and quasiparabolic sets

R. M. Green, Tianyuan Xu

Let $W$ be a simply laced Weyl group of finite type and rank $n$ . If $W$ has type $E_{7}$ , $E_{8}$ , or $D_{n}$ for $n$ even, then the root system of $W$ has subsystems of type $n A_{1}$ . Th…

Minimum distance and decoding of Coxeter codes

Perfect matchings, Fano planes, and orthogonal bases of type E8​

Generalized Rothe diagrams for orthogonal roots

Branching rules of minuscule representations via a new partial order

Orthogonal roots, Macdonald representations, and quasiparabolic sets

Perfect matchings, Fano planes, and orthogonal bases of type $E_{8}$