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The permutation π of [n] = {1, 2, . . . , n} contains the permutation σ of [k] = {1, 2, . . . , k} (written σ ≤ π) if π has a subsequence of length k order isomorphic to σ. For example, π = 391867452 (written in list, or one-line notation) contains σ = 51342, as can be seen by considering the subsequence 91672 (= π(2), π(3), π(5), π(6), π(9)). A permutation(More)
Choose n points from the unit circle — no two with the same x-coordinate or y-coordinate (we call such a set of points generic; another term is noncorectilinear) — label them 1–n by height, reading bottom-to-top, and record these labels reading left-to-right. This operation produces a permutation. For example, the set of points shown below on the left gives(More)
BACKGROUND Carotid endarterectomy (CEA) reduces the risk of stroke in patients with internal carotid stenosis of 50-99 per cent. This study assessed national surgical practice through audit of CEA procedures and outcomes. METHODS This was a prospective cohort study of UK surgeons performing CEA, using clinical audit data collected continuously and(More)
OBJECTIVE Guidelines recommend that patients suffering an ischaemic transient ischaemic attack (TIA) or stroke caused by carotid artery stenosis should undergo carotid endarterectomy (CEA) within 14 days. METHOD The degree to which UK vascular units met this standard was examined and whether rapid interventions were associated with procedural risks. The(More)
A selection of points drawn from a convex polygon, no two with the same vertical or horizontal coordinate, yields a permutation in a canonical fashion. We characterise and enumerate those permutations which arise in this manner and exhibit some interesting structural properties of the permutation class they form. We conclude with a permutation analogue of(More)
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