Publications of Michael E. Hoffman

Cohomology endomorphisms and fixed-point-free maps

  1. S. Allen Broughton, Michael E. Hoffman, and William H. Homer, `The height of two-dimensional cohomology classes of complex flag manifolds,' Canadian Mathematical Bulletin 26 (1983), 498-502. MR 85f:57027; Zbl 493.57026.
  2. Michael E. Hoffman, `Endomorphisms of the cohomology of complex Grassmannians,' Transactions of the American Mathematical Society 281 (1984), 745-760. MR 85f:57028; Zbl 566.14022.
  3. Michael E. Hoffman, `On fixed point free maps of the complex flag manifold,' Indiana University Mathematics Journal 33 (1984), 249-255. MR 85j:57062; Zbl 506.55003.
  4. Michael E. Hoffman and William H. Homer, `On cohomology automorphisms of complex flag manifolds,' Proceedings of the American Mathematical Society 91 (1984), 643-648. MR 85m:57028; Zbl 604.57029.
  5. Michael E. Hoffman, `Noncoincidence index of manifolds,' Pacific Journal of Mathematics 115 (1984), 373-383. MR 86a:55001; Zbl 558.55003.
  6. Michael E. Hoffman, `Free actions of abelian groups on a Cartesian power of an even sphere,' Canadian Mathematical Bulletin 30 (1987), 358-362. MR 88h:57037; Zbl 596.57024.
  7. Michael E. Hoffman, `Homological restrictions on free group actions,' Indiana University Mathematics Journal 37 (1988), 379-387. MR 89k:57079; Zbl 664.57017.
  8. Michael E. Hoffman, `Noncoincidence index, free group actions, and the fixed point property for manifolds,' Pacific Journal of Mathematics 136 (1989), 129-144. MR 90a:55006; Zbl 707.55001.

Generalized Chebyshev polynomials

  1. Michael E. Hoffman and Wm. Douglas Withers, `Generalized Chebyshev polynomials associated with affine Weyl groups,' Transactions of the American Mathematical Society 308 (1988), 91-104. MR 89m:33017; Zbl 681.323020.

Multiple zeta values and related algebra

  1. Michael E. Hoffman, `Multiple harmonic series', Pacific Journal of Mathematics 152 (1992), 275-290. MR 92i:11089; Zbl 763.11037.
  2. Michael E. Hoffman and Courtney Moen, `Sums of triple harmonic series,' Journal of Number Theory 60 (1996), 329-331. MR 98a:11113; Zbl 863.11051.
  3. Michael E. Hoffman, `The algebra of multiple harmonic series,' Journal of Algebra 194 (1997), 477-495. MR 99e:11119; Zbl 881.11067.
  4. Michael E. Hoffman, `Quasi-shuffle products,' Journal of Algebraic Combinatorics 11 (2000), 49-68. MR 2001f:05157 ; Zbl 959.16021.
  5. Michael E. Hoffman, `Periods of mirrors and multiple zeta values,' Proceedings of the American Mathematical Society 130 (2002), 971-974. MR 2002k:14068 ; Zbl 994.32020.
  6. Michael E. Hoffman and Yasuo Ohno, `Relations of multiple zeta values and their algebraic expression,' Journal of Algebra 262 (2003), 332-347. MR 2004c:11163 ; Zbl 1139.11322.
  7. Michael E. Hoffman, `The Hopf algebra structure of multiple harmonic sums,' Nuclear Physics B (Proceedings Supplement) 135 (2004), 215-219. MR 2005i:11125 .
  8. Michael E. Hoffman, `Algebraic aspects of multiple zeta values,' in Zeta Functions, Topology and Quantum Physics (Developments in Mathematics vol. 14), T. Aoki et. al. (eds.), Springer, New York, 2005, pp. 51-74. MR 2006g:11185 ; Zbl 1170.11324.
  9. Michael E. Hoffman, `Quasi-symmetric functions, multiple zeta values, and rooted trees,' Oberwolfach Reports 3 (2006), 1259-1262.
  10. Michael E. Hoffman, `A character on the quasi-symmetric functions coming from multiple zeta values,' Electronic Journal of Combinatorics 15(1) (2008), #R97 (21 pages). MR 2010m:05335 ; Zbl 1163.05334.
  11. Michael E. Hoffman, `Quasi-symmetric functions and mod p multiple harmonic sums,' Kyushu Journal of Mathematics 69 (2015), 345-366. MR 3443040; Zbl 06519983.
  12. Michael E. Hoffman, `Sums of products of Riemann zeta tails,' Mediterranean Journal of Mathematics, 13 (2016), 2771-2781.
  13. Michael E. Hoffman, `Harmonic-number summation identities, symmetric functions, and multiple zeta values,' Ramanujan Journal, to appear.
  14. Michael E. Hoffman, `On multiple zeta values of even arguments,' International Journal of Number Theory, to appear.

Derivative polynomials

  1. Michael E. Hoffman, `Derivative polynomials for tangent and secant,' American Mathematical Monthly 102 (1995), 23-30. MR 95m:26003; Zbl 834.26002.
  2. Michael E. Hoffman, `Derivative polynomials, Euler polynomials, and associated integer sequences,' Electronic Journal of Combinatorics 6 (1999), #R21 (13 pages). MR 2000c:11027 ; Zbl 933.11005.

Posets, rooted trees, and Hopf algebras

  1. Michael E. Hoffman, `An analogue of covering space theory for ranked posets,' Electronic Journal of Combinatorics 8(1) (2001), #R32 (12 pages). MR 2003d:06004 ; Zbl 1007.06004.
  2. Michael E. Hoffman, `Combinatorics of rooted trees and Hopf algebras,' Transactions of the American Mathematical Society 355 (2003), 3795-3811. MR 2004e:16040 ; Zbl 1048.16023.
  3. Michael E. Hoffman, `(Non)Commutative Hopf algebras of trees and (quasi)symmetric functions,' in Renormalization and Galois Theories (IRMA Lectures in Mathematics and Theoretical Physics vol. 15), A. Connes et. al. (eds.), European Math. Soc. Publ. House, Zürich, 2009, pp. 209-227. MR 2010m:16058 ; Zbl 1183.16029.
  4. Michael E. Hoffman, `Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon,' in Vertex Operator Algebras and Related Areas (Contemporary Mathematics vol. 497), M. Bergvelt et. al. (eds.), American Math. Soc., Providence, 2009, pp. 85-95. MR 2010j:16084 ; Zbl 1184.16039.
  5. Michael E. Hoffman, `Updown categories: generating functions and universal covers,' Discrete Mathematics 339 (2016), 906-922. MR 3431404; Zbl 06517696.


  1. Michael E. Hoffman, `An invariant of finite abelian groups,' American Mathematical Monthly 94 (1987), 664-666. MR 89g:20084.
  2. Michael E. Hoffman, `The bull and the silo: an application of curvature,' American Mathematical Monthly 105 (1998), 55-58. MR 99a:53002; Zbl 908.53001.
  3. Michael E. Hoffman and Courtney Moen, `Sums of generalized harmonic series,' Integers 14 (2014), #A46 (11 pp). MR 3256708; Zbl 1311.11084.

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