Combinatorial study of colored Hurwitz polyz\^etas

TL;DR

This paper explores the algebraic structures of colored Hurwitz polyzeta values, revealing connections with shuffle algebras through combinatorial morphisms and analyzing their product and co-product properties.

Contribution

It introduces two surjective morphisms linking generalized shuffle algebras to colored Hurwitz polyzeta algebras, advancing understanding of their combinatorial and algebraic relationships.

Findings

Identifies two surjective morphisms between algebraic structures.

Analyzes combinatorial aspects of products and co-products.

Establishes structural connections in polyzeta algebra.

Abstract

A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyz\^etas. The combinatorial aspects of the products and co-products involved in these algebras will be examined.