## Vong, Vincent - Combinatorial proofs of freeness of some P-algebras

dmtcs:2514 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Combinatorial proofs of freeness of some P-algebras

Authors: Vong, Vincent

We present new combinatorial methods for solving algebraic problems such as computing the Hilbert series of a free $P$-algebra over one generator, or proving the freeness of a $P$-algebra. In particular, we apply these methods to the cases of dendriform algebras, quadrialgebras and tridendriform algebras, which leads us to prove a conjecture of Aguiar and Loday about the freeness of the quadrialgebra generated by the permutation 12.

Source : oai:HAL:hal-01337796v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Free $P$ -algebras,dendriform algebras,quadrialgebras,evaluation trees,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]