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The formal multiple zeta space we consider with a computer is an$\mathbb{F}_2$-vector space generated by $2^{k-2}$ formal symbols for a givenweight $k$, where the symbols satisfy binary extended double shuffle relations.Up to weight $k=22$, we compute the dimensions of the formal multiple zetaspaces, and verify the dimension conjecture on original extended double shufflerelations of real multiple zeta values. Our computations adopt Gaussian forwardelimination and give information for spaces filtered by depth. We can observethat the dimensions of the depth-graded formal multiple zeta spaces have aPascal triangle pattern expected by the Hoffman mult-indices.

Computations about formal multiple zeta spaces defined by binary extended double shuffle relations