arXiv subjects

Gerard H. E. Duchamp

Publications and source records attributed to Gerard H. E. Duchamp.

3 recordsLinked to original sources

arXiv2016

Structure of Polyzetas and Explicit Representation on Transcendence Bases of Shuffle and Stuffle Algebras

Polyzetas, indexed by words, satisfy shuffle and quasi-shuffle identities. In this respect, one can explore the multiplicative and algorithmic (locally finite) properties of their generating series. In this paper, we construct pairs of bases in duality on which polyzetas are established in order to compute local coordinates in the infinite dimensional Lie groups where their non-commutative generating series live. We also propose new algorithms leading to the ideal of polynomial relations, homogeneous in weight, among polyzetas (the graded kernel) and their explicit representation (as data structures) in terms of irreducible elements.

math.CO↗

arXiv2014

Combinatorial interpretation and proof of Glaisher-Crofton identity

We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function methodology of modern enumerative combinatorics and their applications to computational problems.

math.CO↗

arXiv2008

Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.

math.CO↗