  
  
                                   [1X DifSets [101X
  
  
         [1X an algorithm for enumerating all difference sets in a group [101X
  
  
                                     2.3.1
  
  
                               14 September 2019
  
  
                                  Dylan Peifer
  
  
  
  Dylan Peifer
      Email:    [7Xmailto:djp282@cornell.edu[107X
      Homepage: [7Xhttp://www.math.cornell.edu/~djp282[107X
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe  [5XDifSets[105X  Package implements an algorithm for enumerating all difference
  sets up to equivalence in an arbitrary finite group. The algorithm functions
  by finding difference sums, which are potential images of difference sets in
  quotient  groups  of  the  original group, and searching their preimages. In
  this  way,  the  search space can be dramatically decreased, and searches of
  groups  of  relatively  large  order  (such  as order 64 or order 96) can be
  completed.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0YCopyright © 2017, 2019 Dylan Peifer[133X
  
  [33X[0;0YThis  program  is  free  software:  you can redistribute it and/or modify it
  under  the  terms of the GNU General Public License as published by the Free
  Software  Foundation,  either  version 3 of the License, or (at your option)
  any later version.[133X
  
  [33X[0;0YThis  program is distributed in the hope that it will be useful, but WITHOUT
  ANY  WARRANTY;  without  even  the  implied  warranty  of MERCHANTABILITY or
  FITNESS  FOR  A  PARTICULAR  PURPOSE. See the GNU General Public License for
  more details.[133X
  
  [33X[0;0YYou should have received a copy of the GNU General Public License along with
  this program. If not, see [7Xhttp://www.gnu.org/licenses/[107X.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (DifSets)[101X
  
  1 [33X[0;0YDefinitions[133X
    1.1 [33X[0;0YDifference Sets[133X
    1.2 [33X[0;0YDifference Sums[133X
  2 [33X[0;0YPackage Contents[133X
    2.1 [33X[0;0YThe Main Functions[133X
      2.1-1 DifferenceSets
      2.1-2 DifferenceSums
    2.2 [33X[0;0YSizes[133X
      2.2-1 PossibleDifferenceSetSizes
      2.2-2 DifferenceSetsOfSizeK
      2.2-3 DifferenceSumsOfSizeK
    2.3 [33X[0;0YRefining[133X
      2.3-1 RefiningSeries
      2.3-2 AllRefinedDifferenceSets
      2.3-3 NrAllRefinedSets
      2.3-4 SomeRefinedDifferenceSets
      2.3-5 NrSomeRefinedSets
      2.3-6 AllRefinedDifferenceSums
      2.3-7 NrAllRefinedSums
      2.3-8 SomeRefinedDifferenceSums
      2.3-9 NrSomeRefinedSums
    2.4 [33X[0;0YEquivalence[133X
      2.4-1 EquivalentFreeListOfDifferenceSets
      2.4-2 TranslateFreeListOfDifferenceSets
      2.4-3 EquivalentFreeListOfDifferenceSums
      2.4-4 TranslateFreeListOfDifferenceSums
      2.4-5 SmallestEquivalentDifferenceSet
      2.4-6 SmallestEquivalentFreeListOfDifferenceSets
    2.5 [33X[0;0YTesting[133X
      2.5-1 IsDifferenceSet
      2.5-2 IsDifferenceSum
      2.5-3 IsEquivalentDifferenceSet
      2.5-4 IsEquivalentDifferenceSum
    2.6 [33X[0;0YLoading Results[133X
      2.6-1 CanLoadDifferenceSets
      2.6-2 LoadDifferenceSets
  3 [33X[0;0YResults[133X
    3.1 [33X[0;0YOrder 16 and 36[133X
    3.2 [33X[0;0YOrder 64 and 96[133X
    3.3 [33X[0;0YComments[133X
  
  
  [32X
