Changes between Initial Version and Version 4 of Ticket #15272
 Timestamp:
 03/18/14 17:51:14 (8 years ago)
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Ticket #15272

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new
toneeds_review

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Vít Tuček
 Property Cc nthiery bump added

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Bruhat posets and Bruhat graphs for parabolic subgroups
toBruhat posets and Bruhat graphs for parabolic subgroups of finite Weyl groups

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u/vittucek/ticket/15272

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sage6.1
tosage6.2

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472c0908fba197fe9bb73742caab1ebfcde27b53

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Ticket #15272 – Description
initial v4 1 This patch extends the functionality of bruhat_poset and introduces new parabolic_bruhat_graph for finite Weyl groups.1 This patch adds method minimal_representatives and extends the functionality of bruhat_poset and bruhat_graphs. 2 2 3 3 Let W be a finite Weyl group and let W_S be the subgroup of W generated by reflections associated with a subset S of simple roots. Then the cosets W / W_S have unique representatives of minimal length which are ordered by the Bruhat order of W. Similarly for W_S \ W. These poset structures appear in many places, e.g. intersection cohomology of generalized flag varieties or nilpotent Lie algebra cohomology. 4 4 5 This patch adds a parameters index_set (= S) and side (left / right). 6 7 8  9 10 11 Introducing parabolic_bruhat_graph is ugly. Ideally, one would just extend the existing bruhat_graph. However, this method is based upon bruhat_interval which belongs to categories/coxeter_groups.py 12 13 I was unsure where to put the code, which I haven't written yet nor which I need in the foreseeable future anyway. Since it seems that the best course of action would be to implement class (or category?) for parabolic subroot systems / groups I think that one more method for Weyl group is not much of an issue. 5 This patch adds a parameters index_set (= S), crossed_nodes and side (left / right).