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The probability of rectangular unimodular matrices over $\F_q[x]$
Natural density unimodular matrices Riemann’s zeta function q-zeta function finite field polynomial ring
2011/9/13
Abstract: In this note, we compute the probability that a $k\times n$ matrix can be extended to an $n\times n$ invertible matrix over $\F_q[x]$, which turns out to be $(1-q^{k-n})(1-q^{k-1-n})...(1-q^...