Computing Gröbner bases for quantum permutation groups

Non-commutative Gröbner bases of two-sided ideals are not necessarily finite. In my talk I'll give a closed-form description of a finite and reduced Gröbner base for the two-sided ideal used in the construction of Wang's quantum symmetric group. This further extends the computational toolset for research on quantum symmetric groups, quantum automorphism groups of graphs, matroids and other combinatorial structures. For the construction of the Gröbner bases, we relied on the OSCAR system, with large parts of the proof implemented as computations within OSCAR.

This talk is based on joint work with Leonard Schmitz.