#This file does not even begin to find all of the equivalence classes of sets of 2 patterns of length 4 and 2 patterns of length 5. The computer was not able to enumerate them after >1 day of computation.
#Begin samples of attempting to find enumeration schemes for random sets of patterns (2 length four and 2 length five).

>#VatterR4S5(2,2,100,4,2);#This line represents another run that produced nothing.
VatterR4S5(2,2,100,4,2);
VatterR4S5(2,2,10,5,2);


      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 2, 

        PATTERNS OF LENGTH 4 AND, 2, PATTERNS OF LENGTH 5



            The computation took, 572.280, seconds.



      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 2, 

        PATTERNS OF LENGTH 4 AND, 2, PATTERNS OF LENGTH 5


                           Theorem, 1
        The enumeration scheme of permutations avoiding
 {[3, 4, 2, 1], [4, 3, 1, 2], [3, 2, 5, 4, 1], [4, 3, 2, 5, 1]}
                              is 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

  [[1, 2, 3], {}, {1}], [[1, 3, 2], {[2, 0, 0, 0]}, {1}], 

  [[2, 1, 3], {[2, 0, 0, 0]}, {}], 

  [[2, 3, 1], {[1, 0, 0, 0]}, {3}], 

  [[3, 1, 2], {[2, 0, 0, 0]}, {2}], 

  [[3, 2, 1], {[0, 1, 0, 0]}, {}], 

  [[2, 1, 3, 4], {[2, 0, 0, 0, 0]}, {}], 

  [[2, 1, 4, 3], {[0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}, {1}], 

  [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {2}], 

  [[3, 2, 1, 4], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {2}], 

  [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {2}], [

  [4, 2, 1, 3], 

  {[0, 1, 0, 0, 0], [1, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {}], 

  [[4, 3, 1, 2], {[0, 0, 0, 0, 0]}, {1}], 

  [[4, 3, 2, 1], {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}, {}], 

  [[2, 1, 3, 4, 5], {[2, 0, 0, 0, 0, 0]}, {3}], [[2, 1, 3, 5, 4], 

  {[0, 0, 2, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0], 

  [1, 0, 0, 0, 0, 0]}, {3}], [[2, 1, 4, 5, 3], 

  {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, 

  {5}], 

  [[3, 1, 4, 5, 2], {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, {5}

  ], 

  [[3, 2, 4, 5, 1], {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, {5}

  ], [[4, 2, 1, 3, 5], 

  {[0, 0, 2, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, 

  {2, 3}], [[4, 3, 2, 1, 5], 

  {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, 

  {2}], [[5, 2, 1, 3, 4], {[0, 0, 2, 0, 0, 0], 

  [0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0], 

  [2, 0, 0, 0, 0, 0]}, {4}], [[5, 2, 1, 4, 3], 

  {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, 

  {2, 3}], [[5, 3, 1, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [

  [5, 3, 2, 1, 4], 

  {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, 

  {2}], [[5, 3, 2, 4, 1], {[0, 0, 0, 1, 0, 0], 

  [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}, {4}

  ], [[5, 4, 2, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], 

  [[5, 4, 3, 1, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 4, 3, 2, 1], 

  {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, 

  {2}]}


            The computation took, 495.718, seconds.