Abstract : On some properties of the algebra of planar binary trees. We define an involution which reduces to a block triangular form the Gram matrices of the algebra of planar binary trees. This leads us to conjecture the existence of a tower of algebras admitting the latter as its Grothendieck ring. (C) 2003 Academie des sciences. Publie par Editions scientifiques et medicales Elsevier SAS. Tons droits reserves.
F Hivert, Jean-Christophe Novelli, Jean-Yves Thibon. On some properties of the algebra of planar binary trees. Comptes Rendus Mathématique, Elsevier Masson, 2003, 337 (9), pp.565--568. ⟨10.1016/j.crma.2003.09.021⟩. ⟨hal-00693523⟩