Richard Ehrenborg

I am currently supported by National Security Agency grant H98230-06-1-0072.

Here is my current vita.

Upcoming Invitations, Conferences and Workshops

Convex Sets and their Appplications at Banff International Research Station (4-9 March 2006).

Colloquium at the University of British Columbia (24 March 2006). Also the Discrete Mathematics seminar (21 March 2006).

Combinatorics seminar at the University of Minnesota (31 March 2006).

International Conference on Formal Power Series and Algebraic Combinatorics, San Diego, California (19-23 June 2006).

Geometric and Topological Combinatorics, ICM satellite conference, Madrid, Spain, (31 August - 5 September 2006).

Brandeis-Harvard-MIT-Northeastern joint mathematics colloquium (September 14, 2006).

Geometric Combinatorics special session at the Fall 2006 AMS central sectional meeting in Cincinnati, OH (21-22 October 2006).

Margaret Readdy and I are organizing the special session Algebraic and Analytic Combinatorics at the Fall 2006 AMS eastern sectional meeting in Storrs, CT (28-29 October 2006).

MIT Combinatorics Seminar (23 February 2007).

Visiting Cornell University mid-March 2007. Talk in the Cornell Discrete Geometry and Combinatorics Seminar (March 28, 2007).

Northeastern University's Geometry-Algebra-Singularities-Combinatorics Seminar (April 23, 2007).

Michigan State University's Algebra Seminar (October 26, 2007).

Michigan Undergraduate Mathematics and Midwest Systems Biology Conference (October 27, 2007).

Indiana University's Combinatorics Seminar (November 13, 2007).

Research

• 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, 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. ps.gz
  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 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, to appear in European J. Combin. with M. Readdy. pdf

• Flag vectors of polytopes
  20. 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
  21. The c-2d-index of oriented matroids, J. Combin. Theory Ser. A 80 (1997), 79-105, with L. Billera and M. Readdy. pdf
  22. Coproducts and the cd-index, J. Algebraic Combin. 8 (1998), 273-299, with M. Readdy. pdf
  23. On flag vectors, the Dowling lattice and braid arrangements, Discrete Comput. Geom. 21 (1999), 389-403, with M. Readdy. pdf
  24. Cutting polytopes and flag f-vectors, Discrete Comput. Geom. 23 (2000), 261-271, with D. Johnston, R. Rajagopalan and M. Readdy. pdf
  25. Flags and shellings of Eulerian cubical posets, Ann. Comb. 4 (2000), 199-226, with G. Hetyei. pdf
  26. Monotonicity of the cd-index for polytopes, Math. Z. 233 (2000), 421-441, with L. Billera. pdf
  27. The toric h-vectors of partially ordered sets, Trans. Amer. Math. Soc. 352 (2000), 4515-4531, with M. Bayer. pdf
  28. Inequalities for cd-indices of joins and products of polytopes, Combinatorica 23 (2003), 427-452, with H. Fox. pdf
  29. Lifting inequalities for polytopes, Adv. Math. 193 (2005), 205-222. pdf
  30. 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
  31. Decomposition theorem for the cd-index of Gorenstein* posets, J. Algebraic Combin, 26 (2007), 225-251, with K. Karu. pdf
  32. Affine and toric arrangements, with M. Readdy and M. Slone, pdf

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

• Hyperplane arrangements
  36. On valuations, the characteristic polynomial and complex subspace arrangements, Adv. Math. 134 (1998), 32-42, with M. Readdy. pdf
  37. The Dowling transform of subspace arrangements, J. Combin. Theory Ser. A 91 (2000), 322-333, with M. Readdy. pdf

• Permutation statistics
  38. Mixed volumes and slices of the cube, J. Combin. Theory Ser. A 81 (1998), 121-126, with M. Readdy and E. Steingrímsson. pdf
  39. Maximizing the descent statistic, Ann. Comb. 2 (1998), 111-129, with S. Mahajan. pdf
  40. The excedance set of a permutation, Adv. in Appl. Math. 24 (2000), 284-299, with E. Steingrímsson. pdf
  41. 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
  42. Yet another triangle for the Genocchi numbers, European J. Combin. 21 (2000), 593-600, with E. Steingrímsson. pdf
  43. A probabilistic approach to the descent statistic, J. Combin. Theory Ser. A 98 (2002), 150-162 with M. Levin and M. Readdy. pdf
  44. The asymptotics of almost alternating permutations, Adv. in Appl. Math. 28 (2002), 421-437. pdf

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

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

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

• Miscellaneous
  49. A conceptual proof of Cramer's rule, Math. Magazine 77 (2004), 308. pdf
  50. 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.
  51. 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, Harold Fox, Masahiro Hachimori, Gábor Hetyei, Dan Johnston, Kalle Karu, Sergey Kitaev, Michael Levin, Swapneel Mahajan, Miguel Méndez, Peter Perry, 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.