@article{GuoPaychaZhang2014, author = {Guo, Li and Paycha, Sylvie and Zhang, Bin}, title = {Conical zeta values and their double subdivision relations}, series = {Advances in mathematics}, volume = {252}, journal = {Advances in mathematics}, publisher = {Elsevier}, address = {San Diego}, issn = {0001-8708}, doi = {10.1016/j.aim.2013.10.022}, pages = {343 -- 381}, year = {2014}, abstract = {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.}, language = {en} } @article{Clavier2020, author = {Clavier, Pierre J.}, title = {Double shuffle relations for arborified zeta values}, series = {Journal of algebra}, volume = {543}, journal = {Journal of algebra}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-8693}, doi = {10.1016/j.jalgebra.2019.10.015}, pages = {111 -- 155}, year = {2020}, abstract = {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.}, language = {en} }