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Papers by Alexander Postnikov

  *   Papers listed at AMS MathSciNet

  *   Papers posted to arXiv.org

Papers are listed in the reverse chronological order.

  1. Polypositroids, Thomas Lam, Alexander Postnikov,
    arXiv:2010.07120 [math.CO], 14 Oct 2020.

  2. Universal Tutte polynomial, Olivier Bernardi, Tamas Kalman, Alex Postnikov,
    arXiv:2004.00683 [math.CO], 1 Apr 2020.

  3. Higher secondary polytopes and regular plabic graphs, Pavel Galashin, Alexander Postnikov, Lauren Williams,
    arXiv:1909.05435 [math.CO], 12 Sep 2019.

  4. Coxeter submodular functions and deformations of Coxeter permutahedra, Federico Ardila, Federico Castillo, Christopher Eur, Alexander Postnikov, to appear in Advances Math.
    arXiv:1904.11029 [math.CO], 24 Apr 2019.

  5. Positive Grassmannian and polyhedral subdivisions, Alexander Postnikov, Proc. Internat. Congress Math. (ICM 2018), Rio de Janeiro, Vol. 3, 3167-3196.
    arXiv:1806.05307 [math.CO], 14 Jun 2018.
    PDF (25 pages)

  6. A positive formula for the Ehrhart-like polynomials from root system chip-firing, Sam Hopkins, Alexander Postnikov, Algebraic Combinatorics 2 (2019), no. 6, 1159-1196: jounal version
    arXiv:1803.08472 [math.CO]

  7. Trianguloids and Triangulations of Root Polytopes, Pavel Galashin, Gleb Nenashev, Alexander Postnikov
    arXiv:1803.06239 [math.CO]

  8. Cosmological Polytopes and the Wavefunction of the Universe, Nima Arkani-Hamed, Paolo Benincasa, Alexander Postnikov,
    arXiv:1709.02813 [hep-th]

  9. Root system chip-firing I: Interval-firing, Pavel Galashin, Sam Hopkins, Thomas McConville, Alexander Postnikov, Math. Z. 292 (2019), no. 3-4, 1337-1385.
    arXiv:1708.04850 [math.CO]

  10. Root system chip-firing II: Central-firing, Pavel Galashin, Sam Hopkins, Thomas McConville, Alexander Postnikov, Internat. Math. Res. Not. IMRN.
    arXiv:1708.04849 [math.CO]

  11. Purity and separation for oriented matroids, Pavel Galashin, Alexander Postnikov,
    arXiv:1708.01329 [math.CO]

  12. Proof of a conjecture of Bergeron, Ceballos and Labbe, Darij Grinberg, Alexander Postnikov, New York J. Math. 23 (2017), 1581-1610.
    arXiv:1603.03138 [math.CO]

  13. Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs, Tamas Kalman, Alexander Postnikov, Proc. Lond. Math. Soc. (3) 114 (2017), no. 3, 561-588.
    arXiv:1602.04449 [math.CO]

  14. Arrangements of equal minors in the positive Grassmannian, Miriam Farber, A. Postnikov, Advances Math. 300 (2016), 788-834.
    arXiv:1502.01434 [math.CO]

  15. Poset vectors and generalized permutohedra, Dorian Croitoru, SuHo Oh, A. Postnikov
    arXiv:1309.1994 [math.CO]
    PDF (13 pages)

  16. Grassmannian geometry of scattering amplitudes, Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, Jaroslav Trnka, Cambridge University Press, Cambridge, 2016. ix+194 pp.
    Preprint version: Scattering Amplitudes and the Positive Grassmannian:
    arXiv:1212.5605 [hep-th]

  17. On-shell structures of MHV amplitudes beyond the planar limit, Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander Postnikov, Jaroslav Trnka, J. High Energy Phys. 2015, no. 6, 179, 15 pp.
    arXiv:1412.8475 [hep-th]

  18. Two counterexamples for power ideals of arrangements, Federico Ardila, A. Postnikov, Transactions of the American Mathematical Society, 367 (2015), no. 5, 3759-3762.
    arXiv:1211.1368 [math.CO]

  19. Schur times Schubert via the Fomin-Kirillov algebra, Karola Meszaros, Greta Panova, A. Postnikov, Electron. J. Combin. 21 (2014), no. 1, Paper 1.39, 22 pp.
    arXiv:1210.1295 [math.CO]

  20. Alcoved polytopes II, Thomas Lam, A. Postnikov, Lie groups, geometry, and representation theory, 253-272, Progr. Math., 326, Birkhauser/Springer, Cham, 2018.
    arXiv:1202.4015 [math.CO]

  21. Weak separation and plabic graphs, Suho Oh, A. Postnikov, David E Speyer, Proc. Lond. Math. Soc. (3) 110 (2015), no. 3, 721-754.
    arXiv:1109.4434 [math.CO]

  22. Branched polymers and hyperplane arrangements, Karola Meszaros, A. Postnikov, Discrete and Computational Geometry 50 (2013), no. 1, 22-38.
    arXiv:0909.4547 [math.CO]
    PDF (17 pages)

  23. Combinatorics and geometry of power ideals, Federico Ardila, A. Postnikov, Transactions of the American Mathematical Society 362 (2010), no. 8, 4357-4384.
    arXiv:0809.2143 [math.CO]
    PDF (28 pages)

  24. Generalized parking functions, descent numbers, and chain polytopes of ribbon posets, Denis Chebikin, A. Postnikov, Advances in Applied Mathematics 44 (2010), no. 2, 145-154.
    arXiv:0806.0440 [math.CO]
    PDF (11 pages)

  25. Bruhat order, smooth Schubert varieties, and hyperplane arrangements, Suho Oh, A. Postnikov, Hwanchul Yoo, Journal of Combinatorial Theory, Series A. (2008), no. 7, 1156--1166.
    arXiv:0709.3259 [math.CO]
    PDF (14 pages)

  26. A Gelfand model for wreath Products, Ron Adin, A. Postnikov, Yuval Roichman, Israel Journal of Mathematics 179 (2010), 381-402.
    arXiv:0802.2824 [math.RT]

  27. Combinatorial Gelfand models, Ron Adin, A. Postnikov, Yuval Roichman, Journal of Algebra 320 (2008), no. 3, 1311--1325.
    arXiv:0709.3962 [math.RT]
    PDF (13 pages)

  28. Matching polytopes, toric geometry, and the non-negative part of the Grassmannian, A. Postnikov, David Speyer, Lauren Williams, Journal of Algebraic Combinatorics 30 (2009), no. 2, 173-191.
    arXiv:0706.2501 [math.AG]
    PDF (26 pages)

  29. Total positivity, Grassmannians, and networks, A. Postnikov
    arXiv:math/0609764 [math.CO]
    PDF PS (85 pages)   updated version

  30. Faces of generalized permutohedra, A. Postnikov, Victor Reiner, Lauren Williams, Documenta Mathematica13 (2008), 207-273.
    PDF PS (55 pages)

  31. A combinatorial model for crystals of Kac-Moody algebras, Cristian Lenart, A. Postnikov, Transactions of the American Mathematical Society 360 (2008), 4349--4381.
    PDF PS (27 pages)

  32. Generalizations of Abel's and Hurwitz's identities, Alexander Kelmans, A. Postnikov, European Journal of Combinatorics 29 (2008), 1535--1543.
    PDF (9 pages)

  33. What power of two divides a weighted Catalan number? A. Postnikov, Bruce Sagan, Journal of Combinatorial Theory, Series A, 115 no. 5 (2007), 970--977.
    PDF PS (9 pages)

  34. Permutohedra, associahedra, and beyond, A. Postnikov, Int. Math. Res. Not., IMRN 2009, no. 6, 1026-1106.
    PDF PS (59 pages)

  35. Permutohedra, associahedra, and beyond (extended abstract), A. Postnikov, preprint dated November 21, 2004.
    PDF PS (12 pages)

  36. Schur positivity and Schur log-concavity, Thomas Lam, A. Postnikov, Pavlo Pylyavskyy, American Journal of Mathematics 129 (2007), 1611--1622.
    PDF PS (9 pages)

  37. Chains in the Bruhat order, A. Postnikov, Richard Stanley, Journal of Algebraic Combinatorics, (2009) 29: 133--174.
    PDF PS (36 pages)

  38. Alcoved Polytopes I, Thomas Lam, A. Postnikov, Discrete & Computational Geometry 38 no. 3 (2007) 453--478.
    PDF PS (26 pages)

  39. Affine Weyl groups in K-theory and representation theory (extended abstract for FPSAC'04), Cristian Lenart, A. Postnikov.
    PDF (12 pages)

  40. Affine Weyl groups in K-theory and representation theory (full-size version), Cristian Lenart, A. Postnikov, International Mathematics Research Notices (2007), no. 12.
    PDF PS (47 pages)

  41. On the X-rays of permutations, C. Bebeacua, T. Mansour, A. Postnikov, S. Severini: Electronic Notes in Discrete Mathematics 20 (2005), 193-203.
    PDF PS (12 pages)

  42. Quantum Bruhat graph and Schubert polynomials, A. Postnikov: Proceedings of the American Mathematical Society 133 (2005), no. 3, 699--709.
    math.CO/0206077     MR2113918
    PDF PS (10 pages)

  43. Affine approach to quantum Schubert calculus, A. Postnikov: Duke Mathematical Journal, 128 (2005), no. 3, 473-509.
    math.CO/0205165     MR2145741
    PDF (33 pages)

  44. Smoothness of Schubert varieties via patterns in root systems, Sara Billey, A. Postnikov: Advances in Applied Mathematics 34 (2005), 447-466.
    math.CO/0205179     MR2123545
    PDF (17 pages)

  45. Trees, parking functions, syzygies, and deformations of monomial ideals, A. Postnikov, Boris Shapiro: Transactions of the American Mathematical Society 356 (2004), 3109-3142.
    math.CO/0301110     MR2052943
    PDF PS (33 pages)

  46. PP-wave string interactions from perturbative Yang-Mills theory , N. R. Constable, D. Z. Freedman, M. Headrick, S.  Minwalla, L. Motl, A. Postnikov, W. Skiba: The Journal of High Energy Physics, (2002), no. 7, 017, 56 pp.
    hep-th/0205089     MR1940728
    PDF PS (56 pages)

  47. Syzygies of oriented matroids, Isabella Novik, A. Postnikov, Bernd Sturmfels: Duke Mathematical Journal 111 (2002), no. 2, 287--317.
    math.CO/0009241     MR1882136
    PDF (23 pages)

  48. A lattice path approach to counting partitions with minimum rank t, A. Burstein, S. Corteel, A. Postnikov, C. Savage: Discrete Mathematics 249 (2002), no. 1-3, 31--39. (Special issue on the 12th Conference on Combinatorics, Graph Theory and Computing.)
    PDF (9 pages)

  49. Symmetries of Gromov-Witten invariants, A. Postnikov: Advances in Algebraic Geometry Motivated by Physics, Contemporary Mathematics 276 (2001), 251--258.
    math.CO/0009174     MR1837121
    PDF PS (8 pages)

  50. On characters of Weyl groups, Ron Adin, A. Postnikov, Yuval Roichman: Discrete Mathematics 226 (2001), no. 1-3, 355--358.
    math.RT/0005021     MR2001j:20008
    PDF (4 pages)

  51. Hecke algebra actions on the coinvariant algebra, Ron Adin, A. Postnikov, Yuval Roichman: Journal of Algebra 233 (2000), no. 2, 594--613.
    math.RT/9908090     MR2001i:20010
    PDF (20 pages)

  52. Littlewood-Richardson coefficients via Yang-Baxter equation, Oleg Gleizer, A. Postnikov: International Mathematics Research Notices 2000, no.14, 741--774.
    math.QA/9909124     MR2001g:20058
    PDF (34 pages)

  53. Deformations of Coxeter hyperplane arrangements, A. Postnikov, Richard Stanley: Journal of Combinatorial Theory, Series A 91 (2000), no. 1-2, 544--597. (Special issue dedicated to G.-C. Rota.)
    math.CO/9712213 (older version of April 1997)     MR1780038
    PDF (54 pages)

  54. Counting Morse curves and links, A. Postnikov, preprint dated December 4, 2000.
    PDF PS (8 pages)

  55. Tree and forest volumes of graphs, Alexander Kelmans, Igor Pak, A. Postnikov: DIMACS Technical Report 2000-03, January 2000.
    PDF PS (31 pages)

  56. Mixed Bruhat operators and Yang-Baxter equations for Weyl groups, Francesco Brenti, Sergey Fomin, A. Postnikov: International Mathematics Research Notices 1999, no. 8, 419--441.
    math.QA/9805079     MR2000e:20067
    PDF (23 pages)

  57. Algebras of curvature forms on homogeneous manifolds, A. Postnikov, Boris Shapiro, Michael Shapiro: in Differential Topology, Infinite-Dimensional Lie Algebras, and Applications: D. B. Fuchs 60th Anniversary Collection, AMS Translations, Series 2 194 (1999), 227--235.
    math.AG/9901075     MR2001a:53079
    PDF PS (9 pages)

  58. On a quantum version of Pieri's formula, A. Postnikov: Advances in Geometry, Progress in Mathematics 172 (1999), 371--383.
    PDF PS (12 pages)

  59. Chern forms on flag manifolds and forests, A. Postnikov, Boris Shapiro, Michael Shapiro: Proceedings of the 10-th International Conference FPSAC'98, Fields Institute, Toronto, 1998.
    PDF PS (5 pages)

  60. A Generalization of Sylvester's identity, Igor Pak, A. Postnikov: Discrete Mathematics 178 (1998), no. 1-3, 277--281.
    PDF (5 pages)

  61. Enumeration in algebra and geometry, A. Postnikov: Ph.D. thesis, MIT, June 1997 (thesis advisor Richard Stanley).
    PDF PS (88 pages)

  62. Quantum Schubert polynomials, Sergey Fomin, Sergei Gelfand, A. Postnikov: Journal of the American Mathematical Society 10 (1997), no. 3, 565--596.
    PDF PS (32 pages)

  63. Intransitive trees, A. Postnikov: Journal of Combinatorial Theory, Series A 77 (1997), no. 2, 360--366.
    PDF (7 pages)

  64. Combinatorics of hypergeometric functions associated with positive roots, Israel M. Gelfand, Mark I. Graev, A. Postnikov: in Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory, Birkhauser, Boston, 1996, 205--221.
    PDF PS (16 pages)

  65. Trees Associated with the Motzkin numbers, Alexander Kuznetsov, Igor Pak, A. Postnikov: Journal of Combinatorial Theory, Series A 76 (1996), no. 1, 145--147.
    PDF (3 pages)

  66. Oscillating tableaux, S_n x S_m-modules, and Robinson-Schensted-Knuth correspondence, Igor Pak, A. Postnikov: Proceedings of the 8-th International Conference FPSAC'96, University of Minnesota, 1996.
    PDF PS (22 pages)

  67. Enumeration of trees and one amazing representation of the symmetric group, Igor Pak, A. Postnikov: Proceedings of the 8-th International Conference FPSAC'96, University of Minnesota, 1996.
    PDF PS (5 pages)

  68. Noncommutative Lagrange theorem and inversion polynomials, Igor Pak, A. Postnikov, Vladimir Retakh: presented at 7-th International Conference FPSAC'95, University of Paris, 1995.
    PDF PS (13 pages)

  69. Transversal matroids and strata on grassmannians, Igor Pak, A. E. Postnikov: Functional Analysis and its Applications 29 (1995), no. 2, 140--143.
    PDF (4 pages)

  70. Enumereation of spanning trees of graphs, Igor Pak, A. Postnikov: preprint dated November 1, 1994.
    PDF PS (18 pages)

  71. Increasing trees and alternating permutations, A. G. Kuznetsov, Igor Pak, A. E. Postnikov: Russian Mathematical Surveys 49 (1994), no. 6, 79--110.

  72. Resolutions for S_n-modules, associated with rim hooks, and combinatorial applications, I. M. Pak, A. E. Postnikov: Functional Analysis and its Applications 28 (1994), no. 2, 132--134.
    PDF (3 pages)

  73. Paths in the Young graph and Robinson-Schensted-Knuth correspondence, A. E. Postnikov: M.S. thesis, Moscow State University, 1993.

  74. Enumeration of spanning trees in some graphs, I. M. Pak, A. E. Postnikov: Russian Mathematical Surveys 45 (1990), no. 3, 220--221.

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Last updated:   February 09, 2024