Rewriting modulo isotopies computes bases for 2-cells in the KLR 2-category that match Khovanov-Lauda conjectures, proving non-degeneracy and thus categorification of Lusztig's integral quantum group.
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Generalized k-chromatic polynomials of graphs are expressed via dimensions of grade spaces in the associated free partially commutative Lie algebra using heaps of pieces.
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Rewriting modulo isotopies in Khovanov-Lauda-Rouquier's categorification of quantum groups
Rewriting modulo isotopies computes bases for 2-cells in the KLR 2-category that match Khovanov-Lauda conjectures, proving non-degeneracy and thus categorification of Lusztig's integral quantum group.
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Generalized chromatic polynomials of graphs from Heaps of pieces
Generalized k-chromatic polynomials of graphs are expressed via dimensions of grade spaces in the associated free partially commutative Lie algebra using heaps of pieces.