Publications of Mark Pankov


Books

  1. Wigner-type theorems for Hilbert Grassmannians,
    London Mathematical Society Lecture Note Series,
    Cambridge University Press 2020.

    Some remarks and corrections

  2. Geometry of semilinear embeddings:Relations to graphs and codes
    World Scientific 2015.

  3. Grassmannians of classical buildings
    World Scientific 2010, Algebra and Discrete Mathematics, Vol. 2.

Preprints and Submitted

  1. with Krzysztof Petelczyc and Mariusz Zynel,
    Symmetric (15,8,4)-designs in terms of the geometry of binary simplex codes of dimension 4, arXiv.

Articles

  1. with Krzysztof Petelczyc and Mariusz Zynel,
    Point-line geometries related to binary equidistant codes,
    Journal of Combinatorial Theory, Series A, 210(2025) 105962.

  2. A non-surjective Wigner-type theorem in terms of equivalent pairs of subspaces,
    Linear Algebra and its Applications 698(2024), 261-271.

  3. with Adam Tyc,
    Chow's theorem for Hilbert Grassmannians as a Wigner-type theorem,
    Linear and Multilinear Algebra (accepted).

  4. with Mariusz Kwiatkowski,
    On maximal cliques in the graph of simplex codes,
    Journal of Geometry 115(2024), art.10.

  5. On the graph of non-degenerate linear $[n,2]_2$ codes,
    Finite Fields and Their Applications 92(2023), 102282.

  6. with Krzysztof Petelczyc and Mariusz Zynel,
    Automorphisms of graphs corresponding to conjugacy classes of finite-rank self-adjoint operators,
    Linear Algebra and its Applications 674(2023), 192-207.

  7. The graphs of non-degenerate linear codes,
    Journal of Combinatorial Theory, Series A 195(2023), 105720.

  8. with Lucijan Plevnik,
    A non-injective version of Wigner's theorem,
    Operator and Matrices 17(2023), 517-524.

  9. Commutativity preserving transformations on conjugacy classes of compact self-adjoint operators,
    Linear Algebra and its Applications 649(2022), 390-407.

  10. with Thomas Vetterlein,
    A geometric approach to Wigner-type theorems,
    Bulletin of the London Mathematical Society, 53(2021), 1653-1662.

  11. with Krzysztof Petelczyc and Mariusz Zynel,
    Automorphisms and some geodesic properties of ortho-Grassmann graphs,
    The Electronic Journal of Combinatorics 28 (2021), P4.49.

  12. with Krzysztof Petelczyc and Mariusz Zynel,
    Generalized Grassmann graphs associated to conjugacy classes of finite-rank self-adjoint operators,
    Linear Algebra and its Applications 627(2021), 1-23.

  13. with Adam Tyc,
    Z-knotted triangulations of surfaces,
    Discrete & Computational Geometry 66(2021), 636-658.

  14. Orthogonality preserving transformations of Hilbert Grassmannians,
    Linear Algebra and its Applications 605(2020), 180-189.

  15. with Mariusz Kwiatkowski,
    The graph of 4-ary simplex codes of dimension 2,
    Finite Fields and Their Applications 67(2020), 101709.

  16. Commutativity preserving transformations on conjugacy classes of finite rank self-adjoint operators,
    Linear Algebra and its Applications 582(2019), 430-439.

  17. with Adam Tyc,
    On two types of Z-monodromy in triangulations of surfaces,
    Discrete Mathematics 342(2019), 2549-2558.

  18. Wigner's type theorem in terms of linear operators which send projections of a fixed rank to projections of other fixed rank,
    Journal of Mathematical Analysis and Applications 474(2019), 1238-1249.

  19. with Adam Tyc,
    Connected sums of z-knotted triangulations,
    European Journal of Combinatorics 80(2019), 326-338,
    Special Issue in Memory of Michel Marie Deza.

  20. with Mariusz Kwiatkowski and Antonio Pasini,
    The graphs of projective codes,
    Finite Fields and Their Applications 54(2018), 15-29.

  21. Geometric version of Wigner's theorem for Hilbert Grassmannians,
    Journal of Mathematical Analysis and Applications 459(2018), 135-144.

  22. with Michel Deza,
    Zigzag structure of thin chamber complexes,
    Discrete & Computational Geometry 59(2018),363-382.

  23. Apartments preserving transformations of Grassmannians of infinite-dimensional vector spaces,
    Linear Algebra and its Applications 531(2017), 498-509.

  24. with Mariusz Kwiatkowski,
    Chow's theorem for linear codes,
    Finite Fields and Their Applications 46(2017), 147--162.

  25. with Mariusz Kwiatkowski,
    Isometric embeddings of polar Grassmannians and metric characterizations of their apartments,
    Journal of Algebraic Combinatorics 45(2017), 777--801.

  26. Orthogonal apartments in Hilbert Grassmanians,
    Linear Algebra and its Applications 506(2016), 168-182.

  27. with Mariusz Kwiatkowski,
    On the distance between linear codes,
    Finite Fields and Their Applications 39(2016), 251-263.

  28. On embeddings of Grassmann graphs in polar Grassmann graphs,
    Linear Algebra and its Applications 488(2016),     184-198 .

  29. A note on automorphisms of halved Cayley graphs of Coxeter systems,
    Ars Mathematica Contemporanea 11(2016), 101-106.

  30. Geometrical characterization of semilinear isomorphisms of vector spaces
    and semilinear homeomorphisms of normed spaces    ,
    Linear and Multilinear Algebra, 63(2015), issue 4, 695-701.

  31. Isometric embeddings of half-cube graphs in half-spin Grassmannians,
    The Electronic Journal of Combinatorics 21(2014), issue 4,     P4.4, 22 pages.

  32. with Wen Liu and Kaishun Wang,
    Transformations of polar Grassmannians preserving certain intersecting relations,
    Journal of Algebraic Combinatorics 40(2014), issue 2, 633-646.

  33. Characterization of isometric embeddings of Grassmann graphs,
    Advances in Geometry 14(2014), issue 1, 91-108.

  34. Characterizations of strong semilinear embeddings in terms of general linear and projective linear groups,
    Linear and Multilinear Algebra 61(2013), 1555-1567.

  35. Automorphisms of infinite Johnson graphs,
    Discrete Mathematics 313(2013), 721-725.

  36. A note on automorphisms of the infinite-dimensional hypercube graph,
    The Electronic Journal of Combinatorics 19(2012), issue 4, #P23.

  37. Embeddings of Grassmann graphs,
    Linear Algebra and its Applications 436(2012), 3413-3424.

  38. Characterization of apartments in polar Grassmannians,
    Bulletin of Belgian Mathematical Society Simon Stevin 19(2012), 345-366.

  39. with Hans Havlicek and Andrzej Matras,
    Geometry of cyclic submodules in a free ternion module,
    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 81(2011), 237-249.

  40. Metric characterization of apartments in dual polar spaces,
    Journal of Combinatorial Theory (Series A) 118(2011), 1313-1321.

  41. Isometric embeddings of Johnson graphs in Grassmann graphs,
    Journal of Algebraic Combinatorics 33(2011), 555-570.

  42. with Mariusz Kwiatkowski,
    Opposite relation on dual polar spaces and half-spin Grassmann spaces,
    Results in Mathematics 54(2009), 301-308.
    This is a part of Master thesis under my supervision.

  43. Order preserving transformations of the Hilbert grassmannian (note on the complex case),
    Archiv der Mathematik (Basel) 90(2008), 528-529.

  44. with Jaroslaw Kosiorek and Andrzej Matras,
    Distance preserving mappings of Grassmann graphs,
    Beitrage zur Algebra und Geometrie 49(2008), 233-242.

  45. Base subsets of polar Grassmannians,
    Journal of Combinatorial Theory (Series A) 114(2007), 1394-1406.

  46. Base subsets of symplectic Grassmannians,
    Journal of Algebraic Combinatorics 26(2007), 143-159.

  47. Order preserving transformations of the Hilbert grassmannian,
    Archiv der Mathematik (Basel) 89(2007), 81-86.

  48. Base subsets of Grassmannians: Infinite-dimensional case,
    European Journal of Combinatorics 28(2007), 26-32.

  49. On the geometry of symplectic involutions,
    Beitrage zur Algebra und Geometrie 47(2006), 435-446.

  50. Geometrical mappings of Grassmannians of linear spaces satisfying the exchange axiom,
    Aequationes Mathematicae 72(2006), 254-268.

  51. with Krszysztof Prazmowski and Mariusz Zynel,
    Geometry of polar grassmann spaces,
    Demonstratio Mathematica 39(2006), 625-637.

  52. On the geometry of linear involutions,
    Advances in Geometry 5(2005), 455-467.

  53. with Krszysztof Prazmowski and Mariusz Zynel,
    Transformations preserving adjacency and base subsets of spine spaces,
    Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 75(2005), 21-50.

  54. with Hans Havlicek,
    Transformations on the product of Grassmann spaces,
    Demonstratio Mathematica 38(2005), 675-688.

  55. Chow's theorem and projective polarities,
    Geometriae Dedicata 107(2004), 17-24.

  56. Mappings of the sets of invariant subspaces of null systems,
    Beitrage zur Algebra und Geometrie 45(2004), 389-399.

  57. A characterization of geometrical mappings of grassmann spaces,
    Results in Mathematics 45(2004), 319-327.

  58. Transformations of Grassmannians preserving the class of base sets,
    Journal of Geometry 79(2004), 169-176.

  59. Transformations of grassmannians and automorphisms of classical groups,
    Journal of Geometry 75(2002), 132-150.

  60. with Sergey Maksimenko and Eugene Polulyakh,
    Representations of compact subsets of $R^{n}$,
    Topology and its Applications 119(2002), 33-39.

  61. Projections of $k$-dimensional subsets of $R^{n}$ onto $k$-dimensional planes
    and irregular subsets of the Grassmanian manifolds    ,
    Topology and its Applications 101(2000), 121-135.

  62. with Eugene Polulyakh,
    Critical points of arbitrary mappings from $R^n$ into $R^m$,
    Funktsional. Anal. i Prilozhen 31(1997), 214-216 (translated in Funct. Anal. Appl.).

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