The Hopf algebra of uniform block permutations |
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Authors: | Marcelo Aguiar Rosa C Orellana |
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Institution: | (1) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;(2) Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA |
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Abstract: | We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results
are closely related to the fact that uniform block permutations form a factorizable inverse monoid. This Hopf algebra contains
the Hopf algebra of permutations of Malvenuto and Reutenauer and the Hopf algebra of symmetric functions in non-commuting
variables of Gebhard, Rosas, and Sagan. These two embeddings correspond to the factorization of a uniform block permutation
as a product of an invertible element and an idempotent one.
Aguiar supported in part by NSF grant DMS-0302423.
Orellana supported in part by the Wilson Foundation. |
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Keywords: | Hopf algebra Factorizable inverse monoid Uniform block permutation Set partition Symmetric functions Schur-Weyl duality |
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