Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited
Gerard H. E. Duchamp, Florent Hivert, Jean-Christophe Novelli,, Jean-Yves Thibon
TL;DR
This paper explores advanced algebraic structures called free quasi-symmetric functions, establishing new identities and formulas that deepen understanding of their bases and algebraic properties.
Contribution
It proves a Cauchy identity for free quasi-symmetric functions and introduces a free Weyl formula and a generalized splitting formula, advancing theoretical knowledge.
Findings
Proved a Cauchy identity for free quasi-symmetric functions
Developed a free Weyl formula
Generalized the splitting formula
Abstract
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Molecular spectroscopy and chirality