×

zbMATH — the first resource for mathematics

On some properties of the algebra of binary trees. (Sur quelques propriétés de l’algèbre des arbres binaires.) (French) Zbl 1029.05033
Summary: 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.

MSC:
05C05 Trees
Software:
OEIS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J.-C. Aval, F. Bergeron, N. Bergeron, Ideals of quasi-symmetric functions and super-covariant polynomials for Sn, Adv. Math., à paraı̂tre · Zbl 1031.05127
[2] Duchamp, G.; Hivert, F.; Thibon, J.-Y., Une généralisation des fonctions quasi-symétriques et des fonctions symétriques non commutatives, C. R. acad. sci. Paris Sér. I math., 328, 12, 1113-1116, (1999) · Zbl 0978.05072
[3] Duchamp, G.; Hivert, F.; Thibon, J.-Y., Noncommutative symmetric functions VI: free quasi-symmetric functions and related algebras, Internat. J. alg. comput., 12, 671-717, (2002) · Zbl 1027.05107
[4] Hivert, F.; Novelli, J.-C.; Thibon, J.-Y., Un analogue du monoı̈de plaxique pour LES arbres binaires de recherche, C. R. acad. sci. Paris Sér. I, 335, 577-580, (2002) · Zbl 1013.05026
[5] Krob, D.; Thibon, J.-Y., Noncommutative symmetric functions IV: quantum linear groups and Hecke algebras at q=0, J. algebraic combin., 6, 4, 339-376, (1997) · Zbl 0881.05120
[6] Loday, J.-L.; Ronco, M.O., Hopf algebra of the planar binary trees, Adv. math., 139, 2, 293-309, (1998) · Zbl 0926.16032
[7] N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/ njas/sequences/, A009766 · Zbl 1044.11108
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.