2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75145We 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.Extended abstractRings and AlgebrasCombinatorics05E99, 16W30text