Richard Ehrenborg

My research is supported by NSF grant DMS 0902063.

Here is my current vita.

Upcoming Invitations, Conferences and Workshops

Speaker at the AMS Special Session on Combinatorial Geometry of Polytopes at the Joint Mathematics Meetings in Boston (January 2012).

Seminar at the George Washington University. (March 2012).

Invited speaker at Rutgers Experimental Mathematics Seminar (February 2011).

Invited to LaCIM (March 2011).

Invited speaker at FPSAC 2011, (June 2011).

Workshop on Symmetry in Graphs, Maps and Polytopes at The Fields Institute (October 2011).

Speaker at the AMS Special Session on Permutations at the Joint Mathematics Meetings in San Francisco (January 2010).

Invited speaker at Southwestern Undergraduate Mathematics Research Conference. (March 2010). See the picture in the Fall 2010 Maxima Newsletter.

Organizer of the Workshop CATS 2010: Combinatorics 2010: Advances, Trends and Speculations. Funded by NSF grant DMS-1024407. The keynote speakers are Sara Billey (U Washington), Patricia Hersh (North Carolina State), Isabella Novik (U Washington) and Stephanie van Willigenburg (U British Columbia). March 26, 2010.

Organizer of the AMS Special Session Advances in Algebraic & Geometric Combinatorics. March 27--28, 2010.

Speaker at 2010 SIAM Conference on Discrete Mathematics.

Member at The Institute for Advanced Study (September 2010 to July 2011).

Invited to participate in the Quasisymmetric Functions Workshop at Banff International Research Station (November 2010).

2006, 2007 2008 and 2009.

Publications

• Coalgebras and Hopf algebras
  1. On posets and Hopf algebras, Adv. Math. 119 (1996), 1--25. pdf
  2. k-Eulerian posets, Order. 18 (2001), 227--236. pdf
  3. Homology of Newtonian coalgebras, European J. Combin. 23 (2002), 919--927, with M. Readdy. pdf

  See also papers listed under the heading Flag vectors of polytopes.

• Combinatorial topology
  4. Generalizations of Baxter's theorem and cubical homology, J. Combin. Theory Ser. A 69 (1995), 233--287, with G. Hetyei.
  5. Non-constructible complexes and the bridge index, European J. Combin. 22 (2001), 475--491, with M. Hachimori. pdf
  6. The topology of the independence complex, European J. Combin. 27 (2006), 906--923, with G. Hetyei. pdf
  7. The complex of non-crossing diagonals of a polygon, J. Combin. Theory Ser. A 117 (2010), 642--649, with B. Braun.

• Enumerative combinatorics and partially ordered sets

  8. Schröder parenthesizations and chordates, J. Combin. Theory Ser. A 67 (1994), 127--139, with M. Méndez.
  9. A bijective proof of infinite variated Good's inversion, Adv. Math. 103 (1994), 221--259, with M. Méndez. pdf
  10. Juggling and applications to q-analogues, Discrete Math. 157 (1996), 107--125, with M. Readdy. pdf
  11. Sheffer posets and r-signed permutations, Ann. Sci. Math. Québec 19 (1995), 173--196, with M. Readdy. pdf
  12. The r-cubical lattice and a generalization of the cd-index, European J. Combin. 17 (1996), 709--725, with M. Readdy. pdf
  13. The Hankel determinant of exponential polynomials, Amer. Math. Monthly 107 (2000), 557--560. pdf
  14. A bijective answer to a question of Zvonkin, Ann. Comb. 4 (2000), 195--197. pdf
  15. Determinants involving q-Stirling numbers, Adv. in Appl. Math. 31 (2003), 630--642. pdf
  16. Enumerative properties of Ferrers graphs, Discrete Comput. Geom. special issue in honor of Louis J. Billera, 32 (2004), 481--492, with S. van Willigenburg. pdf
  17. Classification of the factorial functions of Eulerian binomial and Sheffer posets, J. Combin. Theory Ser. A, 114 (2007), 339--359. with M. Readdy. pdf
  18. The Möbius function of partitions with restricted block sizes, Adv. in Appl. Math. 39 (2007), 283--292, with M. Readdy. pdf
  19. Exponential Dowling structures, European J. Combin. 30 (2009), 311--326, with M. Readdy. pdf
  20. Explicit expressions for the extremal excedance set statistics, European J. Combin. 31 (2010), 270--279, with E. Clark.
  21. On the non-existence of an R-labeling, Order, 28 (2011), 437--442, with M. Readdy. pdf

• Flag vectors of polytopes
  22. The cd-index of zonotopes and arrangements, in Mathematical essays in honor of Gian-Carlo Rota (B. E. Sagan and R. P. Stanley, eds.), Birkhäuser, Boston, 1998, pages 23--40 with L. Billera and M. Readdy. pdf
  23. The c-2d-index of oriented matroids, J. Combin. Theory Ser. A 80 (1997), 79--105, with L. Billera and M. Readdy. pdf
  24. Coproducts and the cd-index, J. Algebraic Combin. 8 (1998), 273--299, with M. Readdy. pdf
  25. On flag vectors, the Dowling lattice and braid arrangements, Discrete Comput. Geom. 21 (1999), 389--403, with M. Readdy. pdf
  26. Cutting polytopes and flag f-vectors, Discrete Comput. Geom. 23 (2000), 261--271, with D. Johnston, R. Rajagopalan and M. Readdy. pdf
  27. Flags and shellings of Eulerian cubical posets, Ann. Comb. 4 (2000), 199--226, with G. Hetyei. pdf
  28. Monotonicity of the cd-index for polytopes, Math. Z. 233 (2000), 421--441, with L. Billera. pdf
  29. The toric h-vectors of partially ordered sets, Trans. Amer. Math. Soc. 352 (2000), 4515--4531, with M. Bayer. pdf
  30. Inequalities for cd-indices of joins and products of polytopes, Combinatorica 23 (2003), 427--452, with H. Fox. pdf
  31. Lifting inequalities for polytopes, Adv. Math. 193 (2005), 205--222. pdf
  32. Inequalities for zonotopes, in Mathematical Sciences Research Institute Publication on Combinatorial and Computational Geometry, (J. E. Goodman, J. Pach and E. Welzl, eds.), Cambridge University Press, Cambridge, England, 2005, pages 277--286. pdf

• Flag vectors of posets
  33. Decomposition theorem for the cd-index of Gorenstein* posets, J. Algebraic Combin. 26 (2007), 225--251, with K. Karu. pdf
  34. The Tchebyshev transforms of the first and second kind, Ann. Comb. 14 (2010), 211--244, with M. Readdy.
  35. Level Eulerian posets, to appear in Graphs and Combinatorics, with G. Hetyei and M. Readdy. pdf

• Flag enumeration on manifolds
  36. Affine and toric arrangements, Discrete Comput. Geom. 41 (2009), 481--512, with M. Readdy and M. Slone, pdf
  37. Euler flag enumeration of Whitney stratified spaces with M. Goresky and M. Readdy, pdf

• Polytopes
  38. The f-vector of the descent polytope, Discrete Comput. Geom. 45 (2011), 410--424, with D. Chebikin.

• Invariant theory
  39. Apolarity and canonical forms for homogeneous polynomials, European J. Combin. 14 (1993), 157--181, with G.-C. Rota. pdf
  40. On apolarity and generic canonical forms, J. Algebra 213 (1999), 167--194. pdf
  41. Canonical forms of two by two by two matrices, J. Algebra 213 (1999), 195--224. pdf

• Hyperplane arrangements
  42. On valuations, the characteristic polynomial and complex subspace arrangements, Adv. Math. 134 (1998), 32--42, with M. Readdy. pdf
  43. The Dowling transform of subspace arrangements, J. Combin. Theory Ser. A 91 (2000), 322--333, with M. Readdy. pdf
  44. A geometric approach to acyclic orientations, Order 26 (2009), 283--288, with M. Slone. pdf

  See also papers listed under the heading Flag vectors of polytopes.

• Permutation statistics
  45. Mixed volumes and slices of the cube, J. Combin. Theory Ser. A 81 (1998), 121--126, with M. Readdy and E. Steingrímsson. pdf
  46. Maximizing the descent statistic, Ann. Comb. 2 (1998), 111--129, with S. Mahajan. pdf
  47. The excedance set of a permutation, Adv. in Appl. Math. 24 (2000), 284--299, with E. Steingrímsson. pdf
  48. A combinatorial proof of the log-concavity of the numbers of permutations with k runs, J. Combin. Theory Ser. A 90 (2000), 293--303, with M. Bóna. pdf
  49. Yet another triangle for the Genocchi numbers, European J. Combin. 21 (2000), 593--600, with E. Steingrímsson. pdf
  50. The asymptotics of almost alternating permutations, Adv. in Appl. Math. 28 (2002), 421--437. pdf
  51. Cyclotomic factors of the descent set polynomial, J. Combin. Theory Ser. A 116 (2009), 247--264, with D. Chebikin, P. Pylyavskyy and M. Readdy

  See also papers listed under the heading Enumerative combinatorics and Partially ordered sets.

• Analytic approaches to permutation enumeration
  52. A probabilistic approach to the descent statistic, J. Combin. Theory Ser. A 98 (2002), 150--162 with M. Levin and M. Readdy. pdf
  53. Asymptotics of the Euler number of bipartite graphs, Adv. in Appl. Math. 44 (2010), 155--167, with Y. Farjoun. pdf
  54. A spectral approach to consecutive pattern-avoiding permutations, J. Comb. 2 (2011), 305--353, with S. Kitaev and P. Perry. pdf

• Geometry
  55. Heron's formula from a Pythagoras-type theorem, The Mathematical Gazette 68 (1984), 124--126.
  56. Ehrhart-Macdonald reciprocity extended, preprint 2005, with M. Beck. pdf

• Material Science
  57. A geometric formulation of the law of Aboav--Weaire in two and three dimensions, Journal of Physics A: Mathematical and Theoretical, 45 (2012), 065001, 1--17, with M. Lazar and J. Mason.
      See also The apparent ordering of foams.

• Combinatorial games
  58. The blind bartender's problem, J. Combin. Theory Ser. A 70 (1995), 249--266, with C. Skinner. pdf
  59. Playing nim on a simplicial complex, Electron J. Combin. 3 (1996), 33 pp. with E. Steingrímsson. pdf

• Miscellaneous
  60. A conceptual proof of Cramer's rule, Math. Magazine 77 (2004), 308. pdf
  61. Decoding the Hamming code, Math Horizons, special issue on Codes, Cryptography and National Security, 13 (2006), April issue, pages 16--17. pdf
      • Here is a pdf file with the seven cards and the base card. Either print the file on a double sided printer, or print the file and run it through a copy machine to make it double sided. Then cut out the cards with a pair of scissors.
  62. Advertise! FOCUS 26 (2006), August/September issue, number 6, pages 28--29. pdf

I have had the pleasure and honor to work with the following people: Margaret Bayer, Matthias Beck, Louis Billera, Miklós Bóna, Benjamin Braun, Denis Chebikin, Eric Clark, Yossi Farjoun, Harold Fox, Mark Goresky, Masahiro Hachimori, Gábor Hetyei, Dan Johnston, Kalle Karu, JiYoon Jung, Sergey Kitaev, Menachem Lazar, Michael Levin, Swapneel Mahajan, Miguel Méndez, Peter Perry, Pavlo Pylyavskyy, Rajmohan Rajagopalan, Margaret Readdy, Gian-Carlo Rota, Chris Skinner, Michael Slone, Einar Steingrímsson and Stephanie van Willigenburg.

See also at my listing at MathSciNet.

Michael Levin recieved Honorable Mention for the Morgan Prize for his work in the paper, "A probabilistic approach to the descent statistic." pdf

Here is a page with links to departments and institutes where I have worked or visited.

Here is a collection of math related links.

Here is a family tree of mathematical descendents of Gian-Carlo Rota.