superprismatic Posted April 16, 2010 Report Share Posted April 16, 2010 Consider the following list of alphabetic sequences: ABCDEFG ABCEGFD ACGFEBD ADEBFGC AEGFBCD AGBCEDF AGFCEBD BAFECDG BCFEDAG BDACFEG BDAGCEF BFDACGE BFEACDG BGCDEFA CAEBFGD CAEFDGB CBFAGDE CDAEFBG CDGEFAB CEDGFAB CFDGAEB DAECGBF DBECAGF DECBAGF DEGBAFC DFAGCEB DGBAECF DGBFACE EAGCDBF EBCFGAD EBDFGCA ECFAGDB ECFGBDA EFBDGCA EGBDCFA FABGDEC FAEGDCB FCDEBAG FDABEGC FEGCDBA FEGDABC FGABDEC GBCAFDE GCADBFE GCFDBEA GDCABFE GEBFACD GFDBCAE GFDEBAC [/code]They are listed in alphabetic order -- [b]NOT[/b] in the order in which they were generated. These were generated using a pair of 7-cycle permutations, P and Q, on 7 objects. Each of these 49 sequences was produces by applying P[sup]i[/sup]Q[sup]j[/sup] to ABCDEFG for all pairs i and j such that 0 < i,j < 8. Your task is to: 1. find such a P and Q which will produce all the sequences. 2. determine how many equivalent pairs of such permutations there are. Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted April 17, 2010 Report Share Posted April 17, 2010 Consider the following list of alphabetic sequences: ABCDEFG ABCEGFD ACGFEBD ADEBFGC AEGFBCD AGBCEDF AGFCEBD BAFECDG BCFEDAG BDACFEG BDAGCEF BFDACGE BFEACDG BGCDEFA CAEBFGD CAEFDGB CBFAGDE CDAEFBG CDGEFAB CEDGFAB CFDGAEB DAECGBF DBECAGF DECBAGF DEGBAFC DFAGCEB DGBAECF DGBFACE EAGCDBF EBCFGAD EBDFGCA ECFAGDB ECFGBDA EFBDGCA EGBDCFA FABGDEC FAEGDCB FCDEBAG FDABEGC FEGCDBA FEGDABC FGABDEC GBCAFDE GCADBFE GCFDBEA GDCABFE GEBFACD GFDBCAE GFDEBAC They are listed in alphabetic order -- NOT in the order in which they were generated. These were generated using a pair of 7-cycle permutations, P and Q, on 7 objects. Each of these 49 sequences was produces by applying PiQj to ABCDEFG for all pairs i and j such that 0 < i,j < 8. Your task is to: 1. find such a P and Q which will produce all the sequences. 2. determine how many equivalent pairs of such permutations there are. Interesting problem Let p be the permutation (7,5,2,6,1,3,4) and q be the permutation (7,6,4,5,2,1,3). The pair P and Q that satisfy the OP can be generated by P = pi Q = qj; i, j = 1,2,..,6 Quote Link to comment Share on other sites More sharing options...
Question
superprismatic
Consider the following list of
alphabetic sequences:
Link to comment
Share on other sites
1 answer to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.