Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
Duhr, Modular forms for three-loop banana integrals , 2502.15325
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A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
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Discrete symmetries of Feynman integrals
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops