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Guess the next polynoms in the sequence (MO vs. AI :), count anticommuting $F_p$-matrices, P. Hrubeš conjecture

Here is a sequence of polynoms - (presumably) counting N-tuples of ANTI-commuting 2x2 matrices over $F_p, p>2$. (That is just the case of 2x2 matrices, and (surprisingly) it is not so easy to see a ...
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