3 papers
math.CO2025
A composition theory for upward planar orders
Xue Dong, Xuexing Lu, Yu Ye
An upward planar order on an acyclic directed graph is a special linear extension of the edge poset of that satisfies the nesting condition. This order was introduced to co…
math.CT2021
Causal Network Condensation
Xuexing Lu, Ziqian Tang
In this paper, we introduce a generalized topological quantum field theory based on the symmetric monoidal category which we call causal network condensation since it can be regard…
math.CT2015
Combinatorics and algebra of tensor calculus
Sen Hu, Xuexing Lu, Yu Ye
In this paper, motivated by the theory of operads and PROPs we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad wh…