TY  - JOUR
A1  - Clavier, Pierre J.
T1  - Double shuffle relations for arborified zeta values
JF  - Journal of algebra
N2  - Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to relate them to multiple zeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborified zeta values are algebra morphisms for these new products on trees.
KW  - Rooted trees
KW  - Multiple zeta values
KW  - Shuffle products
KW  - Rota-Baxter
KW  - algebras
Y1  - 2020
U6  - https://doi.org/10.1016/j.jalgebra.2019.10.015
SN  - 0021-8693
SN  - 1090-266X
VL  - 543
SP  - 111
EP  - 155
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Guo, Li
A1  - Paycha, Sylvie
A1  - Zhang, Bin
T1  - Conical zeta values and their double subdivision relations
JF  - Advances in mathematics
N2  - We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values. In order to achieve the closed cone subdivision relation, we also interpret linear relations among fractions as subdivisions of decorated closed cones. As a generalization of the double shuffle relation of multiple zeta values, we give the double subdivision relation of conical zeta values and formulate the extended double subdivision relation conjecture for conical zeta values.
KW  - Convex cones
KW  - Conical zeta values
KW  - Smooth cones
KW  - Decorated cones
KW  - Subdivisions
KW  - Multiple zeta values
KW  - Shuffles
KW  - Quasi-shuffles
KW  - Fractions with linear poles
KW  - Shintani zeta values
Y1  - 2014
U6  - https://doi.org/10.1016/j.aim.2013.10.022
SN  - 0001-8708
SN  - 1090-2082
VL  - 252
SP  - 343
EP  - 381
PB  - Elsevier
CY  - San Diego
ER  -