Martin Henk

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under construction

  • sparsity and integrality gap transference bounds for integer programs jointly with Iskander Aliev and Marcel Celaya
    accepted for IPCO 2024; arXiv:2311.06605

  • polynomial bounds in Koldobsky's discrete slicing problem jointly with Ansgar Freyer
    to appear in Proc. Amer. Math. Soc. arXiv:2303.15976

  • new bounds for the integer carathéodory rank jointly with Iskander Aliev, Mark Hogan, Stefan Kuhlmann, and Timm Oertel
    SIAM J. Optim., 34(1), 2024, 190--200; arXiv:2211.03150

  • on subspace concentration for dual curvature measures jointly with Katharina Eller
    Advances in Applied Mathematics, 151, 2023, 102581; arXiv:2302.09917

  • Minkowski's successive minima in convex and discrete geometry jointly with Iskander Aliev
    Communications in Mathematics, 2023, 31, 35 - 59; arXiv:2304.00120

  • affine subspace concentration conditions for centered polytopes jointly with Ansgar Freyer and Christian Kipp
    Mathematika, 69(2), 2023, 458 - 472; arXiv:2207.08477

  • on the geometry of elementary flux modes jointly with Alexander Bockmayr and Frederick Wieder
    Journal of Mathematical Biology, 2023, 87:50; biorxiv 2022.09.24.509324

  • on lattice width of lattice-free polyhedra and height of Hilbert bases jointly with Stefan Kuhlmann and Robert Weismantel
    SIAM J. Discrete Math., 36, 2022, no. 3, 1918–1942; arXiv:2110.02893

  • proximity bounds for random integer programs jointly with Marcel Celaya
    Math. Program. (B) (2022). online; Preprint 05-2020 TU Berlin, 2020

  • packing minima and lattice points in convex bodies jointly with Matthias Schymura and Fei Xue
    Moscow Journal of Combinatorics and Number Theory, 10-1, 2021, 25–48; arXiv:2005.02234

  • distance-sparsity transference for vertices of corner polyhedra jointly with Iskander Aliev, Marcel Celaya, and Aled Williams
    SIAM J. Optim., 31(1), 2021, 200 - 216; arXiv:2007.00950

  • bounds on the lattice point enumerator via slices and projections jointly with Ansgar Freyer
    Discrete Comput. Geom. 2022, 67:895–-918; arXiv:2004.14097

  • packings, sausages and catastrophes jointly with Jörg M. Wills
    Beiträge zur Algbera und Geometrie, 62, (2021), 265–280 preprint tu berlin-04/2020; (open access)

  • discrete analogues of John’s theorem jointly with Sören Berg
    Moscow Journal of Combinatorics and Number Theory 8-4 (2019), 367-378; arxiv:1809.08943

  • on successive minima-type inequalities for the polar of a convex body jointly with Fei Xue
    Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 2601–2616; arxiv:1809.08943

  • distances to lattice points in knapsack polyhedra jointly with Iskander Aliev and Timm Oertel
    Math. Programming Series A 182 (2020), 175–-198; arxiv:1805.04592

  • a characterization of dual quermassintegrals and the roots of dual steiner polynomials jointly with David Alonso-Gutiérrez and María A. Hernández Cifre
    Adv. Math. 331 (20), 2018, 565-588; arXiv:1707.01675

  • on the the log-minkowski inequality for simplices and parallelepipeds jointly with Hannes Pollehn
    Acta Math. Hungar. 155 (1), 2018, 141-157.

  • necessary subspace concentration conditions for the even dual minkowski problem jointly with Hannes Pollehn
    Adv. Math. 323, 2018, 114-141 temporary access; arXiv:1703.10528

  • a note on lattice packings via lattice refinements Experimental Mathematics 27(1), 2018, 1-9; preprint tu berlin, update

  • subspace concentration of dual curvature measures jointly with Károly Böröczky and Hannes Pollehn
    J. Differential Geometry 109(3), 2018, 411 - 429; arXiv:1604.07390

  • integrality gaps of integer knapsack problems jointly with Iskander Aliev and Timm Oertel
    IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings, 25-38; arXiv:1611.03768

  • cone-volume measure and stability jointly with Károly J. Böröczky
    Adv. Math. 306, 2017, 24-50; arXiv:1407.7272

  • a discrete version of koldobsky's slicing inequality jointly with Matthew Alexander and Artem Zvavitch
    Israel J. Math. 222(1), 2017, 261–278; arXiv:1511.02702

  • lattice point inequalities for centered convex bodies jointly with Sören Lennart Berg
    SIAM J Discrete Math 30(2), 2016, 1148–1158; arXiv:1505.06444

  • cone-volume measure of general centered convex bodies jointly with Károly J. Böröczky
    Adv. Math., 286, 2016, 703-721.

  • note on adelic triangulations and an adelic blichfeldt-type inequality jointly with Carsten Thiel
    Beiträge Algebra Geom., 57, 2016, 37–49; arXiv:1405.5798

  • on extensions of minkowski's theorem on successive minima jointly with Matthias Henze and Maria Hernandez Cifre
    Forum Math., 28(2), 2016, 311-326; arXiv:1405.4993

  • note on the coefficients of rational ehrhart quasi-polynomials of minkowski sums jointly with Eva Linke
    Online J. Anal. Comb. (10), 2015; pdf

  • cone-volume measures of polytopes jointly with Eva Linke
    Adv. Math., 253, 2014, 50-62; arXiv:1305.5335

  • restricted successive minima jointly with Carsten Thiel
    Pacific J. Math., 269(2), 2014, 341-354; arXiv:1302.1407v2

  • integer points in knapsack polytopes and s-covering radius jointly with Iskander Aliev and Eva Linke
    The Electronic Journal of Combinatorics, 20(2) (2013), #P42, arXiv:1211.3269

  • löwner-john ellipsoids Doc. Math., Extra Volume ISMP (2012) 95-106; peprint uni magdeburg

  • steiner polynomials via ultra-logconcave sequences jointly with Maria A. Hernandez Cifre and Eugenia Saorin
    Commun. Contemp. Math. 14(6), 2012, arXiv:1112.4741v1

  • lll-reduction for integer knapsacks jointly with Iskander Aliev
    J. Comb. Optim. 24(4), 2012, 613-626; arxiv:1012.3182

  • blichfeldt-type inequalities and central symmetry jointly with Matthias Henze and Jörg M. Wills
    Adv. Geom. 11(4), 2011, 731-744; preprint uni magdeburg

  • generalized frobenius numbers: bounds and average behavior jointly with Iskander Aliev and Lenny Fukshansky
    Acta Arith. 155, (2012), 53-62; arxiv:1105.0841

  • notes on lattice points of zonotopes and lattice-face polytopes jointly with Christian Bey, Matthias Henze and Eva Linke
    Discrete Math. 311, 2011, 634-644; arxiv:1006.5574v2

  • on the location of roots of steiner polynomials jointly with Maria A. Hernandez Cifre
    Bull. Braz. Math. Soc., New Series 42 (1), 2011, 153-170, preprint uni magdeburg

  • representing simple d-dimensional polytopes by d polynomials jointly with Gennadiy Averkov
    Math. Prog. (A), 126(2), 2011, 203-230; arXiv:0709.2099v1

  • feasability of integer knapsacks jointly with Iskander Aliev
    SIAM Journal on Optimization 20 (2010), issue 6, 2978-2993; pdf

  • minimal zonotopes containing the crosspolytope jointly with Eva Linke and Jörg M. Wills
    Linear Algebra and its Applications 432 (2010), 2942-2952; preprint 2009/41 uni magdeburg

  • expected frobenius numbers jointly with Iskander Aliev and Aicke Hinrichs
    Journal of Combinatorial Theory, Series A, 118 (2011), 525 - 531; arxiv:0910.02620

  • coverings and compressed lattices jointly with Maria A. Hernandez Cifre
    Symmetry: Culture and Science, 22 (3-4), 2011, 307-316; preprint 2009/39 uni magdeburg

  • integer knapsacks: average behavior of the frobenius numbers jointly with Iskander Aliev
    Mathematics of Operations Research, 34(3), 2009, 698-705; arxiv:0810.0234v1

  • three-dimensional polyhedra can be described by three polynomial inequalities jointly with Gennadiy Averkov
    Discrete Comput. Geom.,42(2), 2009, 166-186; arXiv:0807.2137

  • successive minima and radii jointly with Maria A. Hernandez Cifre
    Canad. Math. Bull., 52(3), 2009, 380-388; preprint 02/2008 uni magdeburg

  • lower bounds on the coefficients of ehrhart polynomials jointly with Makoto Tagami
    European J. Combinat., 30, 2009, 70-83; arXiv:0710.2665v1

  • intrinsic volumes and successive radii jointly with Maria A. Hernandez Cifre
    J. Math. Anal. Appl., 343(2), 2008, 733-742; preprint 29/2007 uni magdeburg

  • a blichfeldt-type inequality for the surface area jointly with Jörg M. Wills
    Mh. Math.,154, 2008, 135-144; arXiv:0705.2088v1

  • notes on the roots of steiner polynomials jointly with Maria A. Hernandez Cifre
    Rev. Mat. Iberoamericana, 24 (2), 2008, 631-644; arXiv:math.MG/0703373
    polynomdarstellungen von polyedern (german) Jahresberichte der DMV, 109, 2007, 51-69; preprint 58/2006 uni magdeburg

  • notes on the roots of ehrhart polynomials jointly with Christian Bey and Jörg M. Wills
    Discrete Comput. Geom., 38 (1), 2007, 81-98; arXiv:math.MG/0606089

  • minkowski's successive minima jointly with Jörg M. Wills
    Proceedings of ''The International Conference on Number Theory and Discrete Geometry'', Chandigarh, 2005; Editors: R. Balasubramanian, S.G. Dani, P.M. Gruber, R.J. Hans-Gill; Ramanujan Mathematical Society, 2008, 129-142; preprint 09/2006 uni magdeburg

  • on the existence of crepant resolutions of gorenstein abelian quotient singularities in dimensions >= 4 jointly with Dimitrios I. Dais and Günter M. Ziegler
    Algebraic and Geometric Combinatorics (Athanasiadis et al., eds.), Contemp. Math. (AMS), 423, 2007, 125-193; arXiv:math.AG/0512619

  • lattice point coverings jointly with George Tsintsifas
    Chinese Advances in Mathematics, 36 (4), 2007, 441-446. preprint 29/2005 uni magdeburg

  • successive minima and best simultaneous diophantine approximations jointly with Iskander Aliev
    Mh. Math., 147 (2), 2006, 95-101; arXiv:math.NT/0503365

  • ehrhart polynomials and successive minima jointly with Achill Schürmann and Jörg M. Wills
    Mathematika, 52 (103/104), 2006, 1-16; arXiv:math.AG/0507528

  • polynomial inequalities representing polyhedra jointly with Hartwig Bosse and Martin Grötschel
    Math. Prog. (A), 103:1, 2005, 35-44; arXiv:math.MG/0307190

  • free planes in lattice sphere packings Adv. Geom. 5, 2005, 137-144; arXiv:math.MG/0308098

  • on the equations defining toric l.c.i. singularities jointly with Dimitrios I. Dais
    Trans. Amer. Math. 535 (12), 2003, 4955 - 4984; arXiv:math.AG/0204172

  • on the representation of polyhedra by polynomial inequalities jointly with Martin Grötschel
    Discrete Comput. Geom. 29 (4), 2003, 485 - 504; arXiv:math.MG/0203268

  • integral decomposition of polyhedra and some applications in mixed integer programming jointly with Matthias Köppe and Robert Weismantel
    Math. Prog. (B). 94, 2003, 193-206; preprint 12/2000 uni magdeburg

  • successive minima and lattice points Rendi. Circ. Matematico Palermo, Serie II, Supppl. 70, 2002, 377-384; arXiv:math.MG/0204158

  • diophantine approximations and integer points of cones jointly with Robert Weismantel
    Combinatorica, 22 (3), 2002, 401 - 408; preprint 29/97 zuse zentrum berlin

  • on free planes in lattice ball packings jointly with Günter M. Ziegler and Chuanming Zong
    London Math. Soc. 34, no. 3, 2002, 284-290; preprint 04/2000 uni magdeburg

    die starke-perfekte-graphen-vermutung (german) jointly with Annegret Wagler
    DMV-Mitteilungen3, 2002, 22-25; preprint

  • segments in ball packings jointly with Chuanming Zong
    Mathematika 47, 2000, 31-38; preprint 30/1999 uni magdeburg

  • densest lattice packings of 3-polytopes jointly with Ulrich Betke
    Computational Geometry 16, no. 3, 2000, 157-186; arXiv:math.MG/9909172

  • on minimal solutions of linear diophantine equations jointly with Robert Weismantel
    Contrib. Algebra and Geometry 41, (1), 2000, 49-55; preprint 02/1999 uni magdeburg

  • kugeln im computer - die kepler vermutung (german) jointly with Günter M. Ziegler
    in Alles Mathematik!, M. Aigner and E. Behrends eds., 2nd ed., Vieweg, 2002; preprint

    la congettura di keplero (italian) in Problemi e teoremi, volume II, C. Bartocci and P. Odifreddi, Eiaudi, Torino, 2008;

    spheres in the computer -- the kepler conjecture (english) in Mathematics Everywhere, M. Aigner and E. Behrends eds., AMS, 2010

  • a counterexample to an integer analogue of carathéodory's theorem jointly with Winfried Bruns, Joseph Gubeladze, Alexander Martin and Robert Weismantel
    J. Reine Angew. Math. 510, 1999, 179-185; preprint sc 98-28 zib

  • random projections of regular polytopes jointly with Károly Böröczky, Jr.
    Arch. Math. 73, 1999, 465-473; preprint sc 97-21 zib

  • macht es der computer möglich? (german) DMV-Mitteilungen 4, 1998, 58-60; preprint

  • all abelian quotient c.i.-singularities admit projective crepant resolutions in all dimensions jointly with Dimitrios I. Dais and Günter M. Ziegler
    Advances in Mathematics 139, 1998, 194-239; arXiv:alg-geom/9704007

  • on crepant resolutions of 2-parameter series of gorenstein cyclic quotient singularities jointly with Dimitrios I. Dais and Utz-Uwe Haus
    Results in Mathematics 33, No. 3/4, 1998, 208-266; arXiv:math.AG/9803096

  • randomized simplex algorithms on klee-minty cubes jointly with Bernd Gärtner and Günter M. Ziegler;
    Combinatorica 18 (3), 1998, 349-372; preprint

  • finite packings of spheres jointly with Ulrich Betke
    Discrete Comput. Geom. 19, 1998 , 197-227; preprint 465-1995 tu berlin

  • note on lattice-point-free convex bodies jointly with Poh Wah Awyong and Paul R. Scott
    Mh. Math. 126, 1998, 7-12; preprint sc-96-44 zib

  • test sets of the knapsack problem and simultaneous diophantine approximatio jointly with Robert Weismantel
    Lecture Notes in Comp. Science 1284, Algorithms -ESA'97, R. Burkard and G. Woeginger eds., Springer, 1997, 271-283; preprint sc-97-13 zib

  • the height of minimal hilbert bases jointly with Robert Weismantel
    Results in Mathemtics, 32, 1997, 298-303; preprint

  • note on shortest and nearest lattice vectors Inform. Process. Lett., 61, 1997, 183-188; preprint 430-1995 tu berlin

  • inradii of simplices jointly with Ulrich Betke and Lydia Tsintsifa
    Discrete Comput. Geom., 17, 1997, 365-375; preprint

  • basic properties of convex polytopes jointly with Jürgen Richter-Gebert and Günter M. Ziegler
    Discrete and Computational Geometry, J.E. Goodman and J. O'Rourke eds., CRC Press, Boca Raton, Florida, 1997, Second Edition, 2004, 355-383; preprint 473-1995 tu berlin with updates

  • radii and the sausage conjecture jointly with Károly Böröczky, Jr.
    Canad. Math. Bull. 38(2), 1995, 156-166;

    finite and infinite packings Habilitationsschrift, Universität Siegen, 1995; preprint

  • a new approach to covering jointly with Ulrich Betke and Jörg M. Wills
    Mathematika, 42, 1995, 251-263; preprint 266-1994 uni siegen

  • sausages are good packings jointly with Ulrich Betke and Jörg M. Wills
    Discrete Comput. Geom., 13, 1995, 297-311;

  • finite and infinite packings jointly with Ulrich Betke and Jörg M. Wills
    J. Reine Angew. Math., 453, 1994, 165-191; preprint 262-1993 uni siegen

  • some inequalities for planar convex figures jointly with George A. Tsintsifas
    El. Math., 49(3), 1994, 120-126; preprint

  • intrinsic volumes and lattice points of crosspolytopes jointly with Ulrich Betke
    Mh. Math. 115, 1993, 27-33; preprint 1992 uni siegen

  • successive-minima-type inequalities jointly with Ulrich Betke and Jörg M. Wills
    Discrete Comput. Geom., 9, 1993, 165-175; preprint 1992 uni siegen

  • a generalization of steinhagen's theorem jointly with Ulrich Betke
    Abh. Math. Sem. Univ. Hamburg, 63, 1993, 165-176; preprint 259-1992 uni siegen

  • approximating the volume of convex bodies jointly with Ulrich Betke
    Discrete Comput. Geom. 10, 1993, 15-21; preprint uni siegen

  • a generalization of jung's theorem Geometriae Dedicata 42, 1992, 235-240; preprint uni siegen

  • estimating sizes of a convex body by successive diameters and widths jointly with Ulrich Betke
    Mathematika 39, 1992, 247-257; preprint 251/1991 uni siegen

    ungleichungen für sukzessive minima und verallgemeinerte in- und umkugelradien Dissertation, Universität Siegen, 1991; preprint

  • linear programming by minimizing distances jointly with Ulrich Betke
    ZOR-Methods and Models of OR, 35, 1991, 299-307.

  • inequalities between successive minima and intrinsic volumes of a convex body Mh. Math., 110, 1990, 279-282.

    ein polynomialer algorithmus zur lösung von linearen optimierungsproblemen mit effizientem abbruchkriterium Diplomarbeit, Universität Siegen, 1988.
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