אודות
Cluster algebras and Poisson geometry Hurwitz numbers and moduli spaces of curves Algorithmic combinatorics
פרסומים
- A Plethora of Cluster Structures on GLn, Gekhtman, M., Shapiro, M. & Vainshtein, A., 2024, In: Memoirs of the American Mathematical Society. 297, 1486, p. 297 1 p.
- Generalized cluster structures related to the Drinfeld double of GLn, Gekhtman, M., Shapiro, M. & Vainshtein, A., Apr 2022, In: Journal of the London Mathematical Society. 105, 3, p. 1601-1633 33 p.
- Periodic Staircase Matrices and Generalized Cluster Structures, Gekhtman, M., Shapiro, M. & Vainshtein, A., 1 Mar 2022, In: International Mathematics Research Notices. 2022, 6, p. 4181-4221 41 p.
- Drinfeld double of G L n and generalized cluster structures:, Gekhtman, M., Shapiro, M. & Vainshtein, A., Mar 2018, In: Proceedings of the London Mathematical Society. 116, 3, p. 429-484 56 p.
- Introduction: Exotic cluster structures on SLn: The cremmer-gervais case, Gekhtman, M., Shapiro, M. & Vainshtein, A., Mar 2017, In: Memoirs of the American Mathematical Society. 246, 1165, p. 1-106 106 p.
- Integrable cluster dynamics of directed networks and pentagram maps, Gekhtman, M., Shapiro, M., Tabachnikov, S. & Vainshtein, A., 10 Sep 2016, In: Advances in Mathematics. 300, p. 390-450 61 p.
- Generalized cluster structure on the Drinfeld double of GLn, Gekhtman, M., Shapiro, M. & Vainshtein, A., 1 Apr 2016, In: Comptes Rendus Mathematique. 354, 4, p. 345-349 5 p.
- Cremmer-Gervais cluster structure on SLn, Gekhtman, M., Shapiro, M. & Vainshtein, A., 8 Jul 2014, In: Proceedings of the National Academy of Sciences of the United States of America. 111, 27, p. 9688-9695 8 p.
- Poisson Structures Compatible with the Cluster Algebra Structure in Grassmannians, Gekhtman, M., Shapiro, M., Stolin, A. & Vainshtein, A., May 2012, In: Letters in Mathematical Physics. 100, 2, p. 139-150 12 p.
- Cluster structures on simple complex lie groups and Belavin-Drinfeld classification, Gekhtman, M., Shapiro, M. & Vainshtein, A., 2012, In: Moscow Mathematical Journal. 12, 2, p. 293-312 20 p.
- Poisson geometry of directed networks in an annulus, Gekhtman, M., Shapiro, M. & Vainshtein, A., 2012, In: Journal of the European Mathematical Society. 14, 2, p. 541-570 30 p.
- Higher pentagram maps, weighted directed networks, and cluster dynamics, Gekhtman, M., Shapiro, M., Tabachnikov, S. & Vainshtein, A., 2012, In: Electronic Research Announcements in Mathematical Sciences. 19, p. 1-17 17 p.
- Generalized Bäfscklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective, Gekhtman, M., Shapiro, M. & Vainshtein, A., Jun 2011, In: Acta Mathematica. 206, 2, p. 245-310 66 p.
- Poisson geometry of directed networks in a disk, Gekhtman, M., Shapiro, M. & Vainshtein, A., Jun 2009, In: Selecta Mathematica, New Series. 15, 1, p. 61-103 43 p.
- Chamber behavior of double Hurwitz numbers in genus 0, Shadrin, S., Shapiro, M. & Vainshtein, A., 15 Jan 2008, In: Advances in Mathematics. 217, 1, p. 79-96 18 p.
- On the properties of the exchange graph of a cluster algebra, Gekhtman, M., Shapiro, M. & Vainshtein, A., 2008, In: Mathematical Research Letters. 15, 2-3, p. 321-330 10 p.
- Erratum: Cluster algebras and weil-petersson forms (Duke Mathematical Journal), Gekhtman, M., Shapiro, M. & Vainshtein, A., 15 Aug 2007, In: Duke Mathematical Journal. 139, 2, p. 407-409 3 p.
- On double Hurwitz numbers in genus 0, Shadrin, S., Shapiro, M. & Vainshtein, A., 2007.
- Rational functions and real Schubert calculus, Eremenko, A., Gabrielov, A., Shapiro, M. & Vainshtein, A., Apr 2006, In: Proceedings of the American Mathematical Society. 134, 4, p. 949-957 9 p.
- Periodic de Bruijn triangles: Exact and asymptotic results, Shapiro, B., Shapiro, M. & Vainshtein, A., 6 Aug 2005, In: Discrete Mathematics. 298, 1-3, p. 321-333 13 p.
- Cluster algebras and Weil-Petersson forms, Gekhtman, M., Shapiro, M. & Vainshtein, A., 1 Apr 2005, In: Duke Mathematical Journal. 127, 2, p. 291-311 21 p.
- The number of connected components in double Bruhat cells for nonsimply-laced groups, Gekhtman, M., Shapiro, M. & Vainshtein, A., Mar 2003, In: Proceedings of the American Mathematical Society. 131, 3, p. 731-739 9 p.
- On the number of connected components in the space of M-polynomials in hyperbolic functions, Shapiro, B. & Vainshtein, A., 2003, In: Advances in Applied Mathematics. 30, 1-2, p. 273-282 10 p.
- Topological classification of generic real rational functions, Natanzon, S., Shapiro, B. & Vainshtein, A., Nov 2002, In: Journal of Knot Theory and its Ramifications. 11, 7, p. 1063-1075 13 p.
- Approximation algorithms for multi-parameter graph optimization problems, Basov, I. & Vainshtein, A., 2002, In: Discrete Applied Mathematics. 119, 1-2, p. 129-138 10 p.
- Counting occurrences of 132 in a permutation, Mansour, T. & Vainshtein, A., 2002, In: Advances in Applied Mathematics. 28, 2, p. 185-195 11 p.
- Restricted 132-Avoiding Permutations, Mansour, T. & Vainshtein, A., Apr 2001, In: Advances in Applied Mathematics. 26, 3, p. 258-269 12 p.
- Hurwitz numbers and intersections on moduli spaces of curves, Ekedahl, T., Lando, S., Shapiro, M. & Vainshtein, A., 2001, In: Inventiones Mathematicae. 146, 2, p. 297-327 31 p.
- Layered restrictions and Chebyshev polynomials, Mansour, T. & Vainshtein, A., 2001, In: Annals of Combinatorics. 5, p. 451-458 8 p.
- The general structure of edge-connectivity of a vertex subset in a graph and its incremental maintenance. Odd case, Dinitz, Y. & Vainshtein, A., 2000, In: SIAM Journal on Computing. 30, 3, p. 753-808 56 p.
- Simply laced coxeter groups and groups generated by symplectic transvections, Shapiro, B., Shapiro, M., Vainshtein, A. & Zelevinsky, A., 2000, In: Michigan Mathematical Journal. 48, SUPPL., p. 531-551 21 p.
- Avoiding maximal parabolic subgroups of Sk, Mansour, T. & Vainshtein, A., 2000, In: Discrete Mathematics and Theoretical Computer Science. 4, 1, p. 67-77 11 p.
- Restricted permutations, continued fractions, and Chebyshev polynomials, Mansour, T. & Vainshtein, A., 2000, In: Electronic Journal of Combinatorics. 7, 1 R, p. 1-9 9 p.
- On Hurwitz numbers and Hodge integrals, Ekedahl, T., Lando, S., Shapiro, M. & Vainshtein, A., 15 Jun 1999, In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 328, 12, p. 1175-1180 6 p.
- Kazhdan-Lusztig polynomials for certain varieties of incomplete flags, Shapiro, B., Shapiro, M. & Vainshtein, A., 1 Feb 1998, In: Discrete Mathematics. 180, 1-3, p. 345-355 11 p.
- Skew-symmetric Vanishing Lattices and Intersections of Schubert Cells, Shapiro, B., Shapiro, M. & Vainshtein, A., 1998, In: International Mathematics Research Notices. 11, p. 563-588 26 p.
- Concavity of weighted arithmetic means with applications, Berenstein, A. & Vainshtein, A., 1 Aug 1997, In: Archiv der Mathematik. 69, 2, p. 120-126 7 p.
- Connected Components in the Intersection of Two Open Opposite Schubert Cells in SLn(ℝ)/B, Shapiro, B., Shapiro, M. & Vainshtein, A., 1997, In: International Mathematics Research Notices. 10, p. 468-493 26 p.
- Asymptotics for Morgan numbers of fractional orders, Kreinin, A. & Vainshtein, A., 5 Dec 1996, In: Discrete Mathematics. 161, 1-3, p. 301-308 8 p.
- Topology of intersections of Schubert cells and Hecke algebra, Shapiro, B., Shapiro, M. & Vainshtein, A., 1 Jun 1996, In: Discrete Mathematics. 153, 1-3, p. 305-318 14 p.
- Minimal enclosing parallelogram with application, Schwarz, C., Teich, J., Vainshtein, A., Welzl, E. & Evans, B. L., 1 Sep 1995, Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995. Association for Computing Machinery, p. 434-435 2 p. (Proceedings of the Annual Symposium on Computational Geometry; vol. Part F129372).
- Locally orientable graphs, cell structures, and a new algorithm for the incremental maintenance of connectivity carcasses, Dinitz, Y. & Vainshtein, A., 22 Jan 1995, Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995. Association for Computing Machinery, p. 302-311 10 p. (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).
- The connectivity carcass of a vertex subset in a graph and its incremental maintenance, Dinitz, Y. E. & Vainshteint, A., 23 May 1994, Proceedings of the 26th Annual ACM Symposium on Theory of Computing, STOC 1994. Association for Computing Machinery, p. 716-725 10 p. (Proceedings of the Annual ACM Symposium on Theory of Computing; vol. Part F129502).
- Singularities on the boundary of the hyperbolicity region, Vainshtein, A. D. & Shapiro, B. Z., Dec 1990, In: Journal of Soviet Mathematics. 52, 4, p. 3326-3337 12 p.
- A convexity property of the Poisson distribution and its application in queueing theory, Berenshtein, A. D., Vainshtein, A. D. & Kreinin, A. Y., Oct 1989, In: Journal of Soviet Mathematics. 47, 1, p. 2288-2292 5 p.
- TRANSFORMATIONS OF POISSON STREAMS AND THEIR APPLICATION TO COMMUNICATION SYSTEMS., Vainshtein, A. D. & Kreinin, A. Y., Oct 1986, In: Problems of Information Transmission. 22, 4, p. 326-334 9 p.
- Some characteristics of multiphase queuing systems with infinitely many channels, Vainshtein, A. D. & Kreinin, A. Y., Mar 1986, In: Journal of Soviet Mathematics. 32, 6, p. 581-594 14 p.
- Higher-dimensional analogs of the theorems of Newton and Ivory, Vainshtein, A. D. & Shapiro, B. Z., Jan 1985, In: Functional Analysis and its Applications. 19, 1, p. 17-20 4 p.