Ellenberg, Libedinsky, Plaza, Simental and Williamson prove that for n=2^m, dyadically well-distributed permutations form a Bruhat interval isomorphic to a hypercube of dimension m·2^(m−1).
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Ellenberg, Libedinsky, Plaza, Simental and Williamson prove that for n=2^m, dyadically well-distributed permutations form a Bruhat interval isomorphic to a hypercube of dimension m·2^(m−1). This has order n log n, within a constant factor of the maximum.
Read original source Original paper, Theorem 1.1 and methodologyarxiv.org
Original report: 2026-01-03Ellenberg, Libedinsky, Plaza, Simental and Williamson prove that for n=2^m, dyadically well-distributed permutations form a Bruhat interval isomorphic to a hypercube of dimension m·2^(m−1). This has order n log n, within a constant factor of the maximum.
If correct, improves a linear construction scale to n log n and connects Bruhat order with low-discrepancy permutations and representation-theoretic applications.
A sourced result with the exact hypotheses, baseline, and AI role stated; verification is assessed separately.
Background review: 2026-10-11. Selected sources:
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