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This paper analyses the feasible sets structure of general mixed integer linear programs (MIPs) and its relationship with the existence of a finite cardinality test set which can be applied in augmentation algorithms. We derive and…

Optimization and Control · Mathematics 2025-09-30 Justo Puerto , Jose A. Ruiz-Alba

Bilevel programs model sequential decision interactions between two sets of players and find wide applications in real-world complex systems. In this paper, we consider a bilevel mixed-integer linear program with binary tender, wherein the…

Optimization and Control · Mathematics 2025-09-03 Bo Zhou , Ruiwei Jiang , Siqian Shen

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the…

Representation Theory · Mathematics 2015-04-14 Angelo Bianchi , Adriano Moura

It is stated that Boolean set algebras with unit V, where V is a union of Cartesian products, are axiomatizable. The axiomatization coincides with that of cylindric polyadic equality algebras (class CPE). This is an algebraic representation…

Logic · Mathematics 2011-04-08 Miklos Ferenczi

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…

Representation Theory · Mathematics 2007-11-17 Andrej V. Roiter , Vladimir V. Sergeichuk

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level…

Combinatorics · Mathematics 2017-12-15 Manuel Aprile , Alfonso Cevallos , Yuri Faenza

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…

Representation Theory · Mathematics 2012-04-11 Erhard Neher , Alistair Savage , Prasad Senesi

Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…

Combinatorics · Mathematics 2025-05-16 J. Pascal Gollin , Jay Lilian Kneip

We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…

Data Structures and Algorithms · Computer Science 2025-11-04 Oscar Defrain , Arthur Ohana , Simon Vilmin

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by…

Optimization and Control · Mathematics 2017-01-03 Matthias Köppe , Quentin Louveaux , Robert Weismantel

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a…

Optimization and Control · Mathematics 2019-03-05 Hamidur Rahman , Ashutosh Mahajan

The goal of this paper is to derive new classes of valid convex inequalities for quadratically constrained quadratic programs (QCQPs) through the technique of lifting. Our first main result shows that, for sets described by one bipartite…

Optimization and Control · Mathematics 2021-06-25 Xiaoyi Gu , Santanu S. Dey , Jean-Philippe P. Richard

In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for…

Machine Learning · Computer Science 2018-06-08 Bastian Bohn , Michael Griebel , Christian Rieger

We analyse the fusion of representations of the triplet algebra, the maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is shown that there exists a finite number of representations which are closed under fusion. These…

High Energy Physics - Theory · Physics 2009-10-30 Matthias R. Gaberdiel , Horst G. Kausch

The classical construction of representations of quivers enables us to consider linear maps between several vector spaces. The mixed representations of quivers helps us to work with linear maps as well as bilinear forms on several vector…

Rings and Algebras · Mathematics 2016-12-23 Artem Lopatin

Polyhedra and spectrahedra over the real numbers, or more generally their images under linear maps, are respectively the feasible sets of linear and semidefinite programming, and form the family of semidefinite-representable sets. This…

Algebraic Geometry · Mathematics 2026-05-13 Corentin Cornou , Simone Naldi , Tristan Vaccon

We prove that over an algebraically closed field there is a representation embedding from the category of classical Kronecker-modules without the simple injective into the category of finite-dimensional modules over any…

Representation Theory · Mathematics 2023-05-30 Klaus Bongartz

Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…

Mathematical Physics · Physics 2023-08-15 Ian Marquette , Junze Zhang , Yao-Zhong Zhang

We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP…

Optimization and Control · Mathematics 2019-10-11 Joey Huchette , Juan Pablo Vielma

Adapting a result of Bazhenov, Kalimullin, and Yamaleev, we show that if a Turing degree $\textbf{d}$ is the degree of categoricity of a computable structure $\mathcal{M}$ and is not the strong degree of categoricity of any computable…

Logic · Mathematics 2026-01-19 Joey Lakerdas-Gayle