Zero-entropy automorphisms satisfy plov(f) ≥ d + k(k+2)/4, with a gap principle showing plov(f) is either d² or at most d(d-2) + 2⌊d/4⌋ for d ≥ 4.
Stanley, Enumerative combinatorics
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A lower bound for polynomial volume growth of automorphisms of zero entropy
Zero-entropy automorphisms satisfy plov(f) ≥ d + k(k+2)/4, with a gap principle showing plov(f) is either d² or at most d(d-2) + 2⌊d/4⌋ for d ≥ 4.