On Comparability of Random Permutations
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On Comparability of Random Permutations
jj|| c E DA Ry I L L ECedarville UniversityI* 1 UNIVERSITY.DigitalCommons(o>CedarvilleFaculty Dissertations2007On Comparability of Random Permutations On Comparability of Random PermutationssAdam J. I lamniettCedarville Univerỉity, ahammett(i?cedan'tlle.eduFollow this and additional works at: http://digitalcommons.cedarville.edu/faculty dissertations 0^ Part of the Mathematics CommonsRecommended CitationHammett, Adam J., 'On Comparability of Random Permutations” (2007). Kwirlfy Diưcrta On Comparability of Random PermutationsMni. 76.http://digitalOn Comparability of Random Permutations
‘edarville, a scnxc of the Centennial Library. It has been accepted for inclusion in Faculty Dissertation* by an authorized administrator of DtgitalCojj|| c E DA Ry I L L ECedarville UniversityI* 1 UNIVERSITY.DigitalCommons(o>CedarvilleFaculty Dissertations2007On Comparability of Random Permutations On Comparability of Random PermutationsTY OF RANDOM PERMUTATIONSDISSERTATIONPresented in Partial Fulfillment of the Requirements forthe Degree Doctor of Philosophy in the GraduateSchool of the Ohio State UniversityByAdam Hammett . B.s.* * * * *The Ohio State University2007Dissertation Committee:Dr. Boris Pit tel. AdvisorDr. Gerald EdgarD On Comparability of Random Permutationsr. Akos SeressApproved byAdvisorGraduate Program in Mathematicshttps://khothuvien.cori!ABSTRACTTwo permutations of [n]{1,2, ...,n} are comparable illOn Comparability of Random Permutations
the Bruhal order if onecan be obtained from the ot her by a sequence of transpositions decreasing t he number of inversions. We show t hat, t he totaljj|| c E DA Ry I L L ECedarville UniversityI* 1 UNIVERSITY.DigitalCommons(o>CedarvilleFaculty Dissertations2007On Comparability of Random Permutations On Comparability of Random Permutationsndently of each other, then P(ĩT < ơ) is of order n-2 at most.. By a direct probabilistic argument we prove p(ir < a) is of order (0.708)" at least, so t hat t here is current ly a wide qualitative gap between the upper and lower bounds.Next, emboldened by a connection with Ferrers diagrams and plan On Comparability of Random Permutationse partitions implicit in Bressoud’s book [13], we return to the Bruhat order upper bound and show that for n-permutations 7T],...,7Tr selected indepenOn Comparability of Random Permutations
dently and uniformly at random,jj|| c E DA Ry I L L ECedarville UniversityI* 1 UNIVERSITY.DigitalCommons(o>CedarvilleFaculty Dissertations2007On Comparability of Random Permutationsjj|| c E DA Ry I L L ECedarville UniversityI* 1 UNIVERSITY.DigitalCommons(o>CedarvilleFaculty Dissertations2007On Comparability of Random PermutationsGọi ngay
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