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Algebra i Analiz, 1992, Volume 4, Issue 2, Pages 161–185 (Mi aa315)  

This article is cited in 47 scientific papers (total in 48 papers)

Research Papers

Finitely additive measures of virtual polyhedra

A. V. Pukhlikov, A. G. Khovanskii

Institute for System Research, Russian Academy of Sciences

Full text: PDF file (1372 kB)

English version:
St. Petersburg Mathematical Journal, 1993, 4:2, 337–356

Bibliographic databases:

Received: 10.06.1991

Citation: A. V. Pukhlikov, A. G. Khovanskii, “Finitely additive measures of virtual polyhedra”, Algebra i Analiz, 4:2 (1992), 161–185; St. Petersburg Math. J., 4:2 (1993), 337–356

Citation in format AMSBIB
\Bibitem{PukKho92}
\by A.~V.~Pukhlikov, A.~G.~Khovanskii
\paper Finitely additive measures of virtual polyhedra
\jour Algebra i Analiz
\yr 1992
\vol 4
\issue 2
\pages 161--185
\mathnet{http://mi.mathnet.ru/aa315}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1182399}
\zmath{https://zbmath.org/?q=an:0791.52010|0778.52006}
\transl
\jour St. Petersburg Math. J.
\yr 1993
\vol 4
\issue 2
\pages 337--356


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Khovanskii, “Sums of Finite Sets, Orbits of Commutative Semigroups, and Hilbert Functions”, Funct. Anal. Appl., 29:2 (1995), 102–112  mathnet  crossref  mathscinet  zmath  isi
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    3. Mikhalkin, G, “Whitney formula in higher dimensions”, Journal of Differential Geometry, 44:3 (1996), 583  mathscinet  zmath  isi
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    5. Chen, BF, “The incidence algebra of polyhedra over the Minkowski algebra”, Advances in Mathematics, 118:2 (1996), 337  crossref  mathscinet  zmath  isi
    6. Chen, BF, “Geometric Dehn-Sommerville relations”, Journal of Combinatorial Theory Series A, 73:1 (1996), 142  crossref  mathscinet  zmath  isi
    7. Brion, M, “The structure of the polytope algebra”, Tohoku Mathematical Journal, 49:1 (1997), 1  mathscinet  zmath  adsnasa  isi
    8. Fulton, W, “Intersection theory on toric varieties”, Topology, 36:2 (1997), 335  crossref  mathscinet  zmath  isi
    9. Alesker, S, “Continuous valuations on convex sets”, Geometric and Functional Analysis, 8:2 (1998), 402  crossref  mathscinet  zmath  isi
    10. V. A. Timorin, “An analogue of the Hodge–Riemann relations for simple convex polytopes”, Russian Math. Surveys, 54:2 (1999), 381–426  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Alesker, S, “Continuous rotation invariant valuations on convex sets”, Annals of Mathematics, 149:3 (1999), 977  crossref  mathscinet  zmath  isi
    12. Przeslawski, K, “A functional analytic interpretation of the number of faces of a polyhedron”, Mathematika, 47:93–94 (2000), 1  crossref  mathscinet  zmath  isi
    13. Alesker, S, “On P. McMullen's conjecture on translation invariant valuations”, Advances in Mathematics, 155:2 (2000), 239  crossref  mathscinet  zmath  isi
    14. Pukhlikov, AV, “A Gauss-Ostrogradskii theorem for integral transforms over the Euler characteristic - To the memory of professor Anatolii Platonovich Prudnikov”, Integral Transforms and Special Functions, 9:4 (2000), 299  crossref  mathscinet  zmath  isi
    15. A. G. Khovanskii, D. Novikov, “$L$-convex-concave sets in real projective space and $L$-duality”, Mosc. Math. J., 3:3 (2003), 1013–1037  mathnet  crossref  mathscinet  zmath
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    19. B. Ya. Kazarnovskii, ““Newton polyhedra” of distributions”, Izv. Math., 68:2 (2004), 273–289  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. Alexandrov, V, “Minkowski-type and Alexandrov-type theorems for polyhedral herissons”, Geometriae Dedicata, 107:1 (2004), 169  crossref  mathscinet  zmath  isi
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    22. Alesker, S, “The multiplicative structure on continuous polynomial valuations”, Geometric and Functional Analysis, 14:1 (2004), 1  crossref  mathscinet  zmath  isi
    23. Berenstein A., Kazhdan D., “Geometric and unipotent crystals II: From unipotent bicrystals to crystal bases”, Israel Mathematical Conference Proceedings - QUANTUM GROUPS: PROCEEDINGS OF A CONFERENCE IN MEMORY OF JOSEPH DONIN, Contemporary Mathematics Series, 433, 2004, 13–88  isi
    24. Panina, G, “New counterexamples to A. D. Alexandrov's hypothesis”, Advances in Geometry, 5:2 (2005), 301  crossref  mathscinet  zmath  isi
    25. Karshon, Y, “Euler-Maclaurin with remainder for a simple integral polytope”, Duke Mathematical Journal, 130:3 (2005), 401  crossref  mathscinet  zmath  isi
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    27. G. Yu. Panina, “Algebra mnogogrannikov”, Matem. prosv., ser. 3, 10, Izd-vo MTsNMO, M., 2006, 109–131  mathnet
    28. Proc. Steklov Inst. Math., 252 (2006), 212–224  mathnet  crossref  mathscinet
    29. Alesker, S, “Theory of valuations on manifolds, I. Linear spaces”, Israel Journal of Mathematics, 156 (2006), 311  crossref  mathscinet  zmath  isi
    30. Knyazeva M.G., “Ot virtualnykh mnogogrannikov k klassicheskim sedlovym poverkhnostyam”, Izv. vysshikh uchebnykh zavedenii. Priborostroenie, 49:11 (2006), 24–28
    31. St. Petersburg Math. J., 19:1 (2008), 137–158  mathnet  crossref  mathscinet  zmath  isi
    32. V. M. Buchstaber, T. E. Panov, N. Ray, “Spaces of polytopes and cobordism of quasitoric manifolds”, Mosc. Math. J., 7:2 (2007), 219–242  mathnet  crossref  mathscinet  zmath
    33. Agapito, J, “New polytope decompositions and Euler-Maclaurin formulas for simple integral polytopes”, Advances in Mathematics, 214:1 (2007), 379  crossref  mathscinet  zmath  isi
    34. Karshon, Y, “Exact Euler-Maclaurin formulas for simple lattice polytopes”, Advances in Applied Mathematics, 39:1 (2007), 1  crossref  mathscinet  zmath  isi
    35. M. G. Knyazeva, G. Yu. Panina, “On non-isotopic saddle hedgehogs”, Russian Math. Surveys, 63:5 (2008), 968–969  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    36. Knyazeva, M, “An illustrated theory of hyperbolic virtual polytopes”, Central European Journal of Mathematics, 6:2 (2008), 204  crossref  mathscinet  zmath  isi
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    39. M. G. Knyazeva, “A new example of hyperbolic virtual polytope”, J. Math. Sci. (N. Y.), 175:5 (2011), 509–516  mathnet  crossref
    40. J. Math. Sci. (N. Y.), 175:5 (2011), 591–599  mathnet  crossref
    41. Kiumars Kaveh, A. G. Khovanskii, “Newton polytopes for horospherical spaces”, Mosc. Math. J., 11:2 (2011), 265–283  mathnet  mathscinet
    42. Panina G., “Around a. D. Alexandrov's Uniqueness Theorem for Convex Polytopes”, Adv. Geom., 12:4 (2012), 621–637  crossref  isi
    43. G. Yu. Panina, “Cyclopermutohedron”, Proc. Steklov Inst. Math., 288 (2015), 132–144  mathnet  crossref  crossref  isi  elib
    44. G. Yu. Panina, I. Streinu, “Virtual polytopes”, Russian Math. Surveys, 70:6 (2015), 1105–1165  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    45. I. Yu. Makhlin, “Brion's Theorem for Gelfand–Tsetlin Polytopes”, Funct. Anal. Appl., 50:2 (2016), 98–106  mathnet  crossref  crossref  mathscinet  isi  elib
    46. Esterov A., “Characteristic Classes of Affine Varieties and Plucker Formulas For Affine Morphisms”, J. Eur. Math. Soc., 20:1 (2018), 15–59  crossref  isi
    47. Grigory D. Solomadin, “Quasitoric totally normally split manifolds”, Proc. Steklov Inst. Math., 302 (2018), 358–379  mathnet  crossref  crossref  mathscinet  isi  elib
    48. Evgeniy K. Leinartas, Olga A. Shishkina, “The discrete analog of the Newton–Leibniz formula in the problem of summation over simplex lattice points”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 503–508  mathnet  crossref
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