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Original Articles

Hopf Algebras of Heap Ordered Trees and Permutations

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Pages 453-459 | Received 12 Aug 2007, Published online: 09 Feb 2009

REFERENCES

  • Aguiar , M. , Sottile , F. ( 2005 ). Cocommutative Hopf algebras of permutations and trees . J. Algebraic Combinatorics 22 : 451 – 470 .
  • Grossman , R. L. , Larson , R. G. ( 1989 ). Hopf-algebraic structure of families of trees . J. Algebra 126 : 184 – 210 .
  • Hivert , F. , Novelli , J.-C. , Thibon , J.-Y. Commutative Hopf algebras of permutations and trees . arXiv:math/0502456v1 .
  • Malvenuto , C. , Reutenauer , C. ( 1995 ). Duality between quasi-symmetric functions and the Solomon descent algebra . J. Algebra 177 : 967 – 982 .
  • Solomon , L. ( 1976 ). A formula in the group ring of a coxeter group . J. Algebra 41 : 255 – 268 .
  • Communicated by M. Cohen.

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