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1

A characterization of constant width in Minkowski planes

Gennadiy Averkov, Horst Martini

Journal:

Aequationes Mathematicae

Year:

2004

Language:

english

File:

PDF, 164 KB

english, 2004

2

Largest integral simplices with one interior integral point: Solution of Hensley's conjecture and related results

Averkov, Gennadiy, Krümpelmann, Jan, Nill, Benjamin

Journal:

Advances in Mathematics

Year:

2015

Language:

english

File:

PDF, 832 KB

english, 2015

3

Approximation of Corner Polyhedra with Families of Intersection Cuts

Averkov, Gennadiy, Basu, Amitabh, Paat, Joseph

Journal:

SIAM Journal on Optimization

Year:

2018

Language:

english

File:

PDF, 484 KB

english, 2018

4

Detecting and reconstructing centrally symmetric sets from the autocorrelation: Two discrete cases

Gennadiy Averkov

Journal:

Applied Mathematics Letters

Year:

2009

Language:

english

File:

PDF, 435 KB

english, 2009

5

On planar convex bodies of given Minkowskian thickness and least possible area

Gennadiy Averkov

Journal:

Archiv der Mathematik

Year:

2005

Language:

english

File:

PDF, 125 KB

english, 2005

6

Constant Minkowskian width in terms of double normals

Gennadiy Averkov

Journal:

Journal of Geometry

Year:

2003

Language:

english

File:

PDF, 139 KB

english, 2003

7

A monotonicity lemma in higher dimensions

Gennadiy Averkov

Journal:

Journal of Geometry

Year:

2006

Language:

english

File:

PDF, 109 KB

english, 2006

8

Three-Dimensional Polyhedra Can Be Described by

Gennadiy Averkov, Martin Henk

Journal:

Discrete & Computational Geometry

Year:

2009

Language:

english

File:

PDF, 616 KB

english, 2009

9

Embedding metric spaces into normed spaces and estimates of metric capacity

Gennadiy Averkov, Nico Düvelmeyer

Journal:

Monatshefte für Mathematik

Year:

2007

Language:

english

File:

PDF, 131 KB

english, 2007

10

Description of polygonal regions by polynomials of bounded degree

Gennadiy Averkov, Christian Bey

Journal:

Monatshefte für Mathematik

Year:

2011

Language:

english

File:

PDF, 163 KB

english, 2011

11

Representing simpled-dimensional polytopes bydpolynomials

Gennadiy Averkov, Martin Henk

Journal:

Mathematical Programming

Year:

2011

Language:

english

File:

PDF, 562 KB

english, 2011

12

On pyramids and reducedness

Gennadiy Averkov, Horst Martini

Journal:

Periodica Mathematica Hungarica

Year:

2008

Language:

english

File:

PDF, 96 KB

english, 2008

13

Inequalities for the lattice width of lattice-free convex sets in the plane

Gennadiy Averkov, Christian Wagner

Journal:

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

Year:

2012

Language:

english

File:

PDF, 475 KB

english, 2012

14

On the Reconstruction of Planar Lattice-Convex Sets from the Covariogram

Averkov, Gennadiy, Langfeld, Barbara

Journal:

Discrete & Computational Geometry

Year:

2012

Language:

english

File:

PDF, 852 KB

english, 2012

15

On the Size of Lattice Simplices with a Single Interior Lattice Point

Averkov, Gennadiy

Journal:

SIAM Journal on Discrete Mathematics

Year:

2012

Language:

english

File:

PDF, 258 KB

english, 2012

16

On finitely generated closures in the theory of cutting planes

Gennadiy Averkov

Journal:

Discrete Optimization

Year:

2012

Language:

english

File:

PDF, 229 KB

english, 2012

17

A proof of Lovász’s theorem on maximal lattice-free sets

Gennadiy Averkov

Journal:

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

Year:

2013

Language:

english

File:

PDF, 124 KB

english, 2013

18

Constructive Proofs of some Positivstellensätze for Compact Semialgebraic Subsets of ℝd

Gennadiy Averkov

Journal:

Journal of Optimization Theory and Applications

Year:

2013

Language:

english

File:

PDF, 415 KB

english, 2013

19

Retrieving Convex Bodies from Restricted Covariogram Functions

Gennadiy Averkov and Gabriele Bianchi

Journal:

Advances in Applied Probability

Year:

2007

File:

PDF, 1.58 MB

2007

20

On the Convergence of the Affine Hull of the Chvátal--Gomory Closures

Averkov, Gennadiy, Conforti, Michele, Del Pia, Alberto, Di Summa, Marco, Faenza, Yuri

Journal:

SIAM Journal on Discrete Mathematics

Year:

2013

Language:

english

File:

PDF, 245 KB

english, 2013

21

On Maximal $S$-Free Sets and the Helly Number for the Family of $S$-Convex Sets

Averkov, Gennadiy

Journal:

SIAM Journal on Discrete Mathematics

Year:

2013

Language:

english

File:

PDF, 240 KB

english, 2013

22

Confirmation of Matheron's conjecture on the covariogram of a planar convex body

Averkov, Gennadiy, Bianchi, Gabriele

Journal:

Journal of the European Mathematical Society

Year:

2009

Language:

english

File:

PDF, 221 KB

english, 2009

23

Lifting properties of maximal lattice-free polyhedra

Averkov, Gennadiy, Basu, Amitabh

Journal:

Mathematical Programming

Year:

2015

Language:

english

File:

PDF, 426 KB

english, 2015

24

Maximal Lattice-Free Polyhedra: Finiteness and an Explicit Description in Dimension Three

Averkov, Gennadiy, Wagner, Christian, Weismantel, Robert

Journal:

Mathematics of Operations Research

Year:

2011

Language:

english

File:

PDF, 441 KB

english, 2011

25

Minimal polynomial descriptions of polyhedra and special semialgebraic sets

Averkov, Gennadiy, Bröcker, Ludwig

Journal:

Advances in Geometry

Year:

2012

Language:

english

File:

PDF, 301 KB

english, 2012

26

On reduced polytopes and antipodality

Averkov, Gennadiy, Martini, Horst

Journal:

Advances in Geometry

Year:

2008

Language:

english

File:

PDF, 557 KB

english, 2008

27

Covariograms Generated by Valuations

Averkov, Gennadiy, Bianchi, Gabriele

Journal:

International Mathematics Research Notices

Year:

2015

Language:

english

File:

PDF, 566 KB

english, 2015

28

Characterizations of central symmetry for convex bodies in Minkowski spaces

Averkov, Gennadiy, Makai, Endre, Martini, Horst

Journal:

Studia Scientiarum Mathematicarum Hungarica

Year:

2009

Language:

english

File:

PDF, 299 KB

english, 2009

29

Tight bounds on discrete quantitative Helly numbers

Averkov, Gennadiy, González Merino, Bernardo, Paschke, Ingo, Schymura, Matthias, Weltge, Stefan

Journal:

Advances in Applied Mathematics

Year:

2017

Language:

english

File:

PDF, 621 KB

english, 2017

30

Notions of Maximality for Integral Lattice-Free Polyhedra: The Case of Dimension Three

Averkov, Gennadiy, Krümpelmann, Jan, Weltge, Stefan

Journal:

Mathematics of Operations Research

Year:

2017

Language:

english

File:

PDF, 537 KB

english, 2017

31

Homometry and Direct-Sum Decompositions of Lattice-Convex Sets

Gennadiy Averkov,Barbara Langfeld

Journal:

Discrete & Computational Geometry

Year:

2016

Language:

english

File:

PDF, 922 KB

english, 2016

32

Retrieving convex bodies from restricted covariogram functions

Averkov, Gennadiy, Bianchi, Gabriele

Journal:

Advances in Applied Probability

Year:

2007

Language:

english

File:

PDF, 221 KB

english, 2007

33

On Nearly Equilateral Simplices and Nearly Spaces

Averkov, Gennadiy

Journal:

Canadian Mathematical Bulletin

Year:

2010

Language:

english

File:

PDF, 102 KB

english, 2010

34

Optimal Size of Linear Matrix Inequalities in Semidefinite Approaches to Polynomial Optimization

Averkov, Gennadiy

Journal:

SIAM Journal on Applied Algebra and Geometry

Year:

2019

Language:

english

File:

PDF, 432 KB

english, 2019

35

Equality Case in van der Corput’s Inequality and Collisions in Multiple Lattice Tilings

Averkov, Gennadiy

Journal:

Discrete & Computational Geometry

Year:

2019

Language:

english

File:

PDF, 529 KB

english, 2019

36

On the Inequality for Volume and Minkowskian Thickness

Averkov, Gennadiy

Journal:

Canadian Mathematical Bulletin

Year:

2006

Language:

english

File:

PDF, 179 KB

english, 2006

37

Local optimality of Zaks-Perles-Wills simplices

Averkov, Gennadiy

Journal:

Advances in Applied Mathematics

Year:

2020

File:

PDF, 390 KB

2020

38

Computing the volume of the convex hull of the graph of a trilinear monomial using mixed volumes

Speakman, Emily, Averkov, Gennadiy

Journal:

Discrete Applied Mathematics

Year:

2019

Language:

english

File:

PDF, 359 KB

english, 2019

39

Lattice Simplices with a Fixed Positive Number of Interior Lattice Points: A Nearly Optimal Volume Bound

Averkov, Gennadiy, KrÃ¼mpelmann, Jan, Nill, Benjamin

Journal:

International Mathematics Research Notices

Year:

2020

File:

PDF, 183 KB

2020

40

INEQUALITIES BETWEEN MIXED VOLUMES OF CONVEX BODIES: VOLUME BOUNDS FOR THE MINKOWSKI SUM

Averkov, Gennadiy, Borger, Christopher, Soprunov, Ivan

Journal:

Year:

2020

File:

PDF, 449 KB

2020

41

Classification of Triples of Lattice Polytopes with a Given Mixed Volume

Averkov, Gennadiy, Borger, Christopher, Soprunov, Ivan

Journal:

Discrete & Computational Geometry

Year:

2020

File:

PDF, 780 KB

2020