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When a system has N variables, and we impose k constraints, we generally obtain a system with N-k degrees of freedom. Or at least this is what we expect in a commutative world. In a non-commutative setting, we can end up with more degrees of freedom than N! We explore this phenomenon for certain algebraic structures defined by graphs.

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This page is a summary of: Graphical splittings of Artin kernels, Journal of Group Theory, January 2020, De Gruyter,
DOI: 10.1515/jgth-2020-0124.
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