A-cycle integrals at genus one satisfy linear differential equations whose Picard iterations yield all-order alpha-prime expansions in iterated Eisenstein integrals, with cusp values given by disk integrals.
Lie Elements and Knuth Relations
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abstract
A coplactic class in the symmetric group S_n consists of all permutations in S_n with a given Schensted Q-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of S_n which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Reutenauer and the coplactic algebra introduced by Poirier and Reutenauer is the Solomon descent algebra.
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One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
A-cycle integrals at genus one satisfy linear differential equations whose Picard iterations yield all-order alpha-prime expansions in iterated Eisenstein integrals, with cusp values given by disk integrals.