An Improved Tableau Criterion for Bruhat Order
نویسندگان
چکیده
To decide whether two permutations are comparable in Bruhat order of Sn with the well-known tableau criterion requires ( n 2 ) comparisons of entries in certain sorted arrays. We show that to decide whether x ≤ y only d1 + d2 + . . .+ dk of these comparisons are needed, where {d1, d2, . . . , dk} = {i|x(i) > x(i+1)}. This is obtained as a consequence of a sharper version of Deodhar’s criterion, which is valid for all Coxeter groups.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 3 شماره
صفحات -
تاریخ انتشار 1996