Ihara–Kaneko–Zagier extended double shuffle conjecture

Let $\mathcal{Z}$ be the algebra of multiple zeta values, and let the extended double shuffle relations be the relations obtained by combining the stuffle and shuffle product formulas, including their regularized versions.

Ihara–Kaneko–Zagier conjecture. All algebraic relations in the algebra $\mathcal{Z}$ of multiple zeta values are consequences of the extended double shuffle relations.

The conjecture seeks a complete presentation of the algebra of multiple zeta values by regularized shuffle and stuffle relations. Whether these relations generate all algebraic relations remains open.