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Strachan JD Adler H Alling P Ancher C Anderson H Anderson JL Ashcroft D Barnes CW Barnes G Batha S Bell MG Bell R Bitter M Blanchard W Bretz NL Budny R Bush CE Camp R Caorlin M Cauffman S Chang Z Cheng CZ Collins J Coward G Darrow DS DeLooper J Duong H Dudek L Durst R Efthimion PC Ernst D Fisher R Fonck RJ Fredrickson E Fromm N Fu GY Furth HP Gentile C Gorelenkov N Grek B Grisham LR Hammett G Hanson GR Hawryluk RJ Heidbrink W Herrmann HW Hill KW Hosea J Hsuan H Janos A Jassby DL Jobes FC 《Physical review letters》1994,72(22):3526-3529
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Wong KL Bitter M Hammett GW Heidbrink W Hendel H Kaita R Scott S Strachan JD Tait G Bell MG Budny R Bush C Chan A Coonrod J Efthimion PC England AC Eubank HP Fredrickson E Furth HP Goldston RJ Grek B Grisham L Hawryluk RJ Hill KW Johnson D Kamperschroer J Kugel H Ma C Mansfield D Manos D McCune DC McGuire K Medley SS Mueller D Nieschmidt E Owens DK Paré VK Park H Ramsey A Rasmussen D Roquemore AL Schivell J Sesnic S Taylor G Williams MD Zarnstorff MC 《Physical review letters》1985,55(23):2587-2590
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S. M. Edmonds N. Birnbaum G. H. Walden und L. P. Hammett 《Fresenius' Journal of Analytical Chemistry》1941,122(5-6):215
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Two permutations of are comparable in the Bruhat order if one is closer, in a natural way, to the identity permutation, , than the other. We show that the number of comparable pairs is of order at most, and at least. For the related weak order, the corresponding bounds are and , where . In light of numerical experiments, we conjecture that for each order the upper bound is qualitatively close to the actual number of comparable pairs.
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Hawryluk RJ Adler H Alling P Ancher C Anderson H Anderson JL Ashcroft D Barnes CW Barnes G Batha S Bell MG Bell R Bitter M Blanchard W Bretz NL Budny R Bush CE Camp R Caorlin M Cauffman S Chang Z Cheng CZ Collins J Coward G Darrow DS DeLooper J Duong H Dudek L Durst R Efthimion PC Ernst D Fisher R Fonck RJ Fredrickson E Fromm N Fu GY Furth HP Gentile C Gorelenkov N Grek B Grisham LR Hammett G Hanson GR Heidbrink W Herrmann HW Hill KW Hosea J Hsuan H Janos A Jassby DL Jobes FC Johnson DW 《Physical review letters》1994,72(22):3530-3533