18 citations · 51 across the 11 of their papers we have counts for
11 papers
Multiple Dedekind Symbols
Zhongyu Jin, Qingchun Tian, Yuan Zhou
In this paper we study multiple Dedekind symbols and the associated multiple reciprocity functions. There is a bijection between the two sets of them after a normalization. By this…
Facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem
Matthias Köppe, Yuan Zhou
We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were kn…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VII. Inverse semigroup theory, closures, decomposition of perturbations
Robert Hildebrand, Matthias Köppe, Yuan Zhou
In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory-Johnson infinite group problem. The non-extreme minimal valid…
All Cyclic Group Facets Inject
Matthias Köppe, Yuan Zhou
We give a variant of Basu-Hildebrand-Molinaro's approximation theorem for continuous minimal valid functions for Gomory-Johnson's infinite group problem by piecewise linear two-slo…
On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem
Matthias Köppe, Yuan Zhou
We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were kn…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. V. Software for the continuous and discontinuous 1-row case
Chun Yu Hong, Matthias Köppe, Yuan Zhou
We present software for investigations with cut-generating functions in the Gomory--Johnson model and extensions, implemented in the computer algebra system SageMath.
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. VI. The curious case of two-sided discontinuous minimal valid functions
Matthias Köppe, Yuan Zhou
We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory--Johnson model which is not extreme, but which is not a convex combination of ot…
Software for cut-generating functions in the Gomory--Johnson model and beyond
Chun Yu Hong, Matthias Köppe, Yuan Zhou
We present software for investigations with cut generating functions in the Gomory-Johnson model and extensions, implemented in the computer algebra system SageMath.
Toward computer-assisted discovery and automated proofs of cutting plane theorems
Matthias Köppe, Yuan Zhou
Using a metaprogramming technique and semialgebraic computations, we provide computer-based proofs for old and new cutting-plane theorems in Gomory--Johnson's model of cut generati…
New computer-based search strategies for extreme functions of the Gomory--Johnson infinite group problem
Matthias Köppe, Yuan Zhou
We describe new computer-based search strategies for extreme functions for the Gomory--Johnson infinite group problem. They lead to the discovery of new extreme functions, whose ex…
An Electronic Compendium of Extreme Functions for the Gomory--Johnson Infinite Group Problem
Matthias Köppe, Yuan Zhou
In this note we announce the availability of an electronic compendium of extreme functions for Gomory--Johnson's infinite group problem. These functions serve as the strongest cut-…