using ordinal representation for generating permutations with a fixed number of inversions in lexicographic order ting kuo department of international trade takming university of science and technology 56 huan shan ...
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...Using ordinal representation for generating permutations with a fixed number of inversions in lexicographic order ting kuo department international trade takming university science and technology huan shan rd sec taipei taiwan tkuo edu tw received april revised november accepted december abstract an inversion occurs between pair permutation l n j k if but by new scheme called we propose algorithm the set all m where cn then derive theorem that can be used to guar antee proposed is optimal meaning it will never visit any unqualified permuta tions beauty lies not result itself rather its arithmetical ability wide applicability keywords references r d dutton sorted discrete applied mathematics vol pp e knuth art computer programming volume sorting searching second edition addison wesley b h margolius journal integer sequences article sedgewick algorithms reading ma fascicle tuples addi son generation methods acm computing surveys no t walsh loop free sequencing bounded compositions combin...