Geodesic
POTENTIALS OF A FROBENIUS-LIKE STRUCTURE
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 681-693

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DOI

This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame, which encompasses families of arrangements. The frame uses the notion of matroids. For the proof of the existence of the potentials, a power series ansatz is made. The proof that it works requires that certain decompositions of tuples of coordinate vector fields are related by certain elementary transformations. This is shown with a nontrivial result on matroid partition. 
HERTLING, CLAUS; VARCHENKO, ALEXANDER. POTENTIALS OF A FROBENIUS-LIKE STRUCTURE. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 681-693. doi: 10.1017/S0017089517000374
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     author = {HERTLING, CLAUS and VARCHENKO, ALEXANDER},
     title = {POTENTIALS {OF} {A} {FROBENIUS-LIKE} {STRUCTURE}},
     journal = {Glasgow mathematical journal},
     pages = {681--693},
     year = {2018},
     volume = {60},
     number = {3},
     doi = {10.1017/S0017089517000374},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000374/}
}
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