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permutationmore about permutation

permutation

 

  3  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Permutation  \Per`mu*ta"tion\,  n.  [L.  permutatio:  cf  F. 
  permutation.  See  {Permute}.] 
  1.  The  act  of  permuting;  exchange  of  the  thing  for  another; 
  mutual  transference;  interchange. 
 
  The  violent  convulsions  and  permutations  that  have 
  been  made  in  property.  --Burke. 
 
  2.  (Math.) 
  a  The  arrangement  of  any  determinate  number  of  things 
  as  units,  objects,  letters,  etc.,  in  all  possible 
  orders  one  after  the  other  --  called  also 
  {alternation}.  Cf  {Combination},  n.,  4. 
  b  Any  one  of  such  possible  arrangements. 
 
  3.  (Law)  Barter;  exchange. 
 
  {Permutation  lock},  a  lock  in  which  the  parts  can  be 
  transposed  or  shifted,  so  as  to  require  different 
  arrangements  of  the  tumblers  on  different  occasions  of 
  unlocking. 
 
  From  WordNet  r  1.6  [wn]: 
 
  permutation 
  n  1:  an  event  in  which  one  thing  is  substituted  for  another  [syn: 
  {substitution},  {transposition},  {replacement},  {switch}] 
  2:  the  act  of  changing  the  arrangement  of  a  given  number  of 
  elements 
  3:  complete  change  in  character  or  condition:  "the 
  permutations...taking  place  in  the  physical  world"-  Henry 
  Miller 
  4:  act  of  changing  the  lineal  order  of  objects  in  a  group 
 
  From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]: 
 
  permutation 
 
    An  ordering  of  a  certain  number  of  elements  of  a 
  given  set 
 
  For  instance,  the  permutations  of  (1,2,3)  are  (1,2,3)  (2,3,1) 
  (3,1,2)  (3,2,1)  (1,3,2)  (2,1,3). 
 
  Permutations  form  one  of  the  canonical  examples  of  a  "{group}" 
  -  they  can  be  composed  and  that  you  can  find  an  inverse 
  permutation  that  reverses  the  action  of  any  given  permutation. 
 
  A  permutation  is  a  {bijection}. 
 
  The  number  of  permutations  of  r  things  taken  from  a  set  of  n 
  is 
 
  n  P  r  =  n!  /  (n-r)! 
 
  where  "n  P  r"  is  usually  written  with  n  and  r  as  subscripts 
  and  n!  is  the  {factorial}  of  n. 
 
  What  the  football  pools  call  a  permutation"  is  not  a 
  permutation  but  a  {combination}  -  the  order  does  not  matter. 
 
  (1995-04-10)




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