Combinatorial Semigroup Bialgebras
Matthieu Deneufch\^atel

TL;DR
This paper introduces a general framework for combinatorial bialgebras based on commutative semigroups, unifying shuffle and stuffle algebras, and explores dual bases and Schützenberger's factorizations.
Contribution
It presents a new unified framework for combinatorial bialgebras using commutative semigroups, encompassing shuffle and stuffle algebras, and applies it to dual bases and factorizations.
Findings
Unified framework for combinatorial bialgebras
Construction of dual bases in this setting
Application to Schützenberger's factorizations
Abstract
This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the shuffle and stuffle algebras. We also consider the problem of constructing pairs of bases in duality and present Sch\"utzenberger's factorisations as an application.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics
