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 Permutations at the Joint Mathematics Meetings in San Francisco (January 2010).

Invited speaker at Southwestern Undergraduate Mathematics Research Conference. (March 2010).

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

Invited to participate in the Geometric Combinatorics Workshop at the Institute for Pure and Applied Mathematics, UCLA (October 2009).

Mathematical Magic. Talk to high school students at at the High School Mathematics Day (17 October 2009).

Colloquium at the George Washington University (20 April 2009).

Talk in the special session "Applications of Algebraic and Geometric Combinatorics" at the 2009 Spring Southeastern Sectional Meeting at North Carolina State (4 April 2009).

2006, 2007 and 2008.

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, European J. Combin. 30 (2009), 311--326, 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, Discrete Comput. Geom., 41 (2009), 481-512, 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
  38. A geometric approach to acyclic orientations, to appear in Order, with M. Slone. pdf

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

• Permutation statistics
  39. Mixed volumes and slices of the cube, J. Combin. Theory Ser. A 81 (1998), 121-126, with M. Readdy and E. Steingrímsson. pdf
  40. Maximizing the descent statistic, Ann. Comb. 2 (1998), 111-129, with S. Mahajan. pdf
  41. The excedance set of a permutation, Adv. in Appl. Math. 24 (2000), 284-299, with E. Steingrímsson. pdf
  42. 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
  43. Yet another triangle for the Genocchi numbers, European J. Combin. 21 (2000), 593-600, with E. Steingrímsson. pdf
  44. A probabilistic approach to the descent statistic, J. Combin. Theory Ser. A 98 (2002), 150-162 with M. Levin and M. Readdy. pdf
  45. 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
  46. Heron's formula from a Pythagoras-type theorem, The Mathematical Gazette 68 (1984), 124-126.
  47. Ehrhart-Macdonald reciprocity extended, preprint 2005, with M. Beck. pdf

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

• Miscellaneous
  50. A conceptual proof of Cramer's rule, Math. Magazine 77 (2004), 308. pdf
  51. 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.
  52. 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, Masahiro Hachimori, Gábor Hetyei, Dan Johnston, Kalle Karu, Sergey Kitaev, 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.