# Commutative monoids up to size 5 CMon_count = [1, 2, 5, 19, 78] # total = 105 CMon_index = [0, 1, 3, 8, 27] CMon_list = [ CMon(e = 0, num = 0, mult = [ [0]]), CMon(e = 0, num = 1, mult = [ [0,1], [1,0]]), CMon(e = 0, num = 2, mult = [ [0,1], [1,1]]), CMon(e = 0, num = 3, mult = [ [0,1,2], [1,0,2], [2,2,2]]), CMon(e = 0, num = 4, mult = [ [0,1,2], [1,1,1], [2,1,1]]), CMon(e = 0, num = 5, mult = [ [0,1,2], [1,1,1], [2,1,2]]), CMon(e = 0, num = 6, mult = [ [0,1,2], [1,1,2], [2,2,1]]), CMon(e = 0, num = 7, mult = [ [0,1,2], [1,2,0], [2,0,1]]), CMon(e = 0, num = 8, mult = [ [0,1,2,3], [1,0,2,3], [2,2,2,2], [3,3,2,2]]), CMon(e = 0, num = 9, mult = [ [0,1,2,3], [1,0,2,3], [2,2,2,2], [3,3,2,3]]), CMon(e = 0, num = 10, mult = [ [0,1,2,3], [1,0,2,3], [2,2,2,3], [3,3,3,2]]), CMon(e = 0, num = 11, mult = [ [0,1,2,3], [1,0,3,2], [2,3,0,1], [3,2,1,0]]), CMon(e = 0, num = 12, mult = [ [0,1,2,3], [1,0,3,2], [2,3,1,0], [3,2,0,1]]), CMon(e = 0, num = 13, mult = [ [0,1,2,3], [1,0,3,2], [2,3,2,3], [3,2,3,2]]), CMon(e = 0, num = 14, mult = [ [0,1,2,3], [1,1,1,1], [2,1,1,1], [3,1,1,1]]), CMon(e = 0, num = 15, mult = [ [0,1,2,3], [1,1,1,1], [2,1,1,1], [3,1,1,2]]), CMon(e = 0, num = 16, mult = [ [0,1,2,3], [1,1,1,1], [2,1,1,1], [3,1,1,3]]), CMon(e = 0, num = 17, mult = [ [0,1,2,3], [1,1,1,1], [2,1,1,2], [3,1,2,3]]), CMon(e = 0, num = 18, mult = [ [0,1,2,3], [1,1,1,1], [2,1,2,1], [3,1,1,3]]), CMon(e = 0, num = 19, mult = [ [0,1,2,3], [1,1,1,1], [2,1,2,2], [3,1,2,2]]), CMon(e = 0, num = 20, mult = [ [0,1,2,3], [1,1,1,1], [2,1,2,2], [3,1,2,3]]), CMon(e = 0, num = 21, mult = [ [0,1,2,3], [1,1,1,1], [2,1,2,3], [3,1,3,2]]), CMon(e = 0, num = 22, mult = [ [0,1,2,3], [1,1,1,1], [2,1,3,0], [3,1,0,2]]), CMon(e = 0, num = 23, mult = [ [0,1,2,3], [1,1,1,3], [2,1,1,3], [3,3,3,1]]), CMon(e = 0, num = 24, mult = [ [0,1,2,3], [1,1,1,3], [2,1,2,3], [3,3,3,1]]), CMon(e = 0, num = 25, mult = [ [0,1,2,3], [1,1,2,2], [2,2,1,1], [3,2,1,1]]), CMon(e = 0, num = 26, mult = [ [0,1,2,3], [1,1,2,3], [2,2,3,1], [3,3,1,2]]), CMon(e = 0, num = 27, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,2,2], [4,4,2,2,2]]), CMon(e = 0, num = 28, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,2,2], [4,4,2,2,3]]), CMon(e = 0, num = 29, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,2,2], [4,4,2,2,4]]), CMon(e = 0, num = 30, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,2,3], [4,4,2,3,4]]), CMon(e = 0, num = 31, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,3,2], [4,4,2,2,4]]), CMon(e = 0, num = 32, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,3,3], [4,4,2,3,3]]), CMon(e = 0, num = 33, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,3,3], [4,4,2,3,4]]), CMon(e = 0, num = 34, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,2], [3,3,2,3,4], [4,4,2,4,3]]), CMon(e = 0, num = 35, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,4], [3,3,2,2,4], [4,4,4,4,2]]), CMon(e = 0, num = 36, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,2,4], [3,3,2,3,4], [4,4,4,4,2]]), CMon(e = 0, num = 37, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,3,3], [3,3,3,2,2], [4,4,3,2,2]]), CMon(e = 0, num = 38, mult = [ [0,1,2,3,4], [1,0,2,3,4], [2,2,2,3,4], [3,3,3,4,2], [4,4,4,2,3]]), CMon(e = 0, num = 39, mult = [ [0,1,2,3,4], [1,0,2,4,3], [2,2,2,2,2], [3,4,2,0,1], [4,3,2,1,0]]), CMon(e = 0, num = 40, mult = [ [0,1,2,3,4], [1,0,2,4,3], [2,2,2,2,2], [3,4,2,1,0], [4,3,2,0,1]]), CMon(e = 0, num = 41, mult = [ [0,1,2,3,4], [1,0,2,4,3], [2,2,2,2,2], [3,4,2,2,2], [4,3,2,2,2]]), CMon(e = 0, num = 42, mult = [ [0,1,2,3,4], [1,0,2,4,3], [2,2,2,2,2], [3,4,2,3,4], [4,3,2,4,3]]), CMon(e = 0, num = 43, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,1,1], [4,1,1,1,1]]), CMon(e = 0, num = 44, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,1,1], [4,1,1,1,2]]), CMon(e = 0, num = 45, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,1,1], [4,1,1,1,4]]), CMon(e = 0, num = 46, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,1,2], [4,1,1,2,1]]), CMon(e = 0, num = 47, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,1,2], [4,1,1,2,2]]), CMon(e = 0, num = 48, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,1,2], [4,1,1,2,3]]), CMon(e = 0, num = 49, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,1,3], [4,1,1,3,4]]), CMon(e = 0, num = 50, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,2,1], [4,1,1,1,2]]), CMon(e = 0, num = 51, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,2,1], [4,1,1,1,4]]), CMon(e = 0, num = 52, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,2,2], [4,1,1,2,2]]), CMon(e = 0, num = 53, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,3,1], [4,1,1,1,4]]), CMon(e = 0, num = 54, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,3,3], [4,1,1,3,3]]), CMon(e = 0, num = 55, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,3,3], [4,1,1,3,4]]), CMon(e = 0, num = 56, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,1], [3,1,1,3,4], [4,1,1,4,3]]), CMon(e = 0, num = 57, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,2], [3,1,1,1,2], [4,1,2,2,4]]), CMon(e = 0, num = 58, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,2], [3,1,1,1,3], [4,1,2,3,4]]), CMon(e = 0, num = 59, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,2], [3,1,1,2,3], [4,1,2,3,4]]), CMon(e = 0, num = 60, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,2], [3,1,1,3,1], [4,1,2,1,4]]), CMon(e = 0, num = 61, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,1,2], [3,1,1,3,3], [4,1,2,3,4]]), CMon(e = 0, num = 62, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,2,2], [3,1,2,3,3], [4,1,2,3,3]]), CMon(e = 0, num = 63, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,2,2], [3,1,2,3,3], [4,1,2,3,4]]), CMon(e = 0, num = 64, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,2,2], [3,1,2,3,4], [4,1,2,4,3]]), CMon(e = 0, num = 65, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,1,2,2], [3,1,2,4,0], [4,1,2,0,3]]), CMon(e = 0, num = 66, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,1,1], [3,1,1,3,1], [4,1,1,1,4]]), CMon(e = 0, num = 67, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,1,1], [3,1,1,3,3], [4,1,1,3,3]]), CMon(e = 0, num = 68, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,1,1], [3,1,1,3,3], [4,1,1,3,4]]), CMon(e = 0, num = 69, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,1,1], [3,1,1,3,4], [4,1,1,4,3]]), CMon(e = 0, num = 70, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,1,2], [3,1,1,3,3], [4,1,2,3,4]]), CMon(e = 0, num = 71, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,2,2], [4,1,2,2,2]]), CMon(e = 0, num = 72, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,2,2], [4,1,2,2,3]]), CMon(e = 0, num = 73, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,2,2], [4,1,2,2,4]]), CMon(e = 0, num = 74, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,2,3], [4,1,2,3,4]]), CMon(e = 0, num = 75, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,3,2], [4,1,2,2,4]]), CMon(e = 0, num = 76, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,3,3], [4,1,2,3,3]]), CMon(e = 0, num = 77, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,3,3], [4,1,2,3,4]]), CMon(e = 0, num = 78, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,3,4], [4,1,2,4,3]]), CMon(e = 0, num = 79, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,2], [3,1,2,4,0], [4,1,2,0,3]]), CMon(e = 0, num = 80, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,4], [3,1,2,2,4], [4,1,4,4,2]]), CMon(e = 0, num = 81, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,2,4], [3,1,2,3,4], [4,1,4,4,2]]), CMon(e = 0, num = 82, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,3,3], [3,1,3,2,2], [4,1,3,2,2]]), CMon(e = 0, num = 83, mult = [ [0,1,2,3,4], [1,1,1,1,1], [2,1,2,3,4], [3,1,3,4,2], [4,1,4,2,3]]), CMon(e = 0, num = 84, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,1,1,4], [3,1,1,1,4], [4,4,4,4,1]]), CMon(e = 0, num = 85, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,1,1,4], [3,1,1,2,4], [4,4,4,4,1]]), CMon(e = 0, num = 86, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,1,1,4], [3,1,1,3,4], [4,4,4,4,1]]), CMon(e = 0, num = 87, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,1,2,4], [3,1,2,3,4], [4,4,4,4,1]]), CMon(e = 0, num = 88, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,2,1,4], [3,1,1,3,4], [4,4,4,4,1]]), CMon(e = 0, num = 89, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,2,2,4], [3,1,2,2,4], [4,4,4,4,1]]), CMon(e = 0, num = 90, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,2,2,4], [3,1,2,3,4], [4,4,4,4,1]]), CMon(e = 0, num = 91, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,2,3,4], [3,1,3,2,4], [4,4,4,4,1]]), CMon(e = 0, num = 92, mult = [ [0,1,2,3,4], [1,1,1,1,4], [2,1,3,0,4], [3,1,0,2,4], [4,4,4,4,1]]), CMon(e = 0, num = 93, mult = [ [0,1,2,3,4], [1,1,1,3,3], [2,1,1,3,3], [3,3,3,1,1], [4,3,3,1,1]]), CMon(e = 0, num = 94, mult = [ [0,1,2,3,4], [1,1,1,3,3], [2,1,1,3,3], [3,3,3,1,1], [4,3,3,1,2]]), CMon(e = 0, num = 95, mult = [ [0,1,2,3,4], [1,1,1,3,3], [2,1,2,3,3], [3,3,3,1,1], [4,3,3,1,1]]), CMon(e = 0, num = 96, mult = [ [0,1,2,3,4], [1,1,1,3,3], [2,1,2,3,4], [3,3,3,1,1], [4,3,4,1,1]]), CMon(e = 0, num = 97, mult = [ [0,1,2,3,4], [1,1,1,3,3], [2,1,2,3,4], [3,3,3,1,1], [4,3,4,1,2]]), CMon(e = 0, num = 98, mult = [ [0,1,2,3,4], [1,1,1,3,4], [2,1,1,3,4], [3,3,3,4,1], [4,4,4,1,3]]), CMon(e = 0, num = 99, mult = [ [0,1,2,3,4], [1,1,1,3,4], [2,1,2,3,4], [3,3,3,4,1], [4,4,4,1,3]]), CMon(e = 0, num = 100, mult = [ [0,1,2,3,4], [1,1,2,2,2], [2,2,1,1,1], [3,2,1,1,1], [4,2,1,1,1]]), CMon(e = 0, num = 101, mult = [ [0,1,2,3,4], [1,1,2,2,4], [2,2,4,4,1], [3,2,4,4,1], [4,4,1,1,2]]), CMon(e = 0, num = 102, mult = [ [0,1,2,3,4], [1,1,2,3,4], [2,2,1,4,3], [3,3,4,1,2], [4,4,3,2,1]]), CMon(e = 0, num = 103, mult = [ [0,1,2,3,4], [1,1,2,3,4], [2,2,1,4,3], [3,3,4,2,1], [4,4,3,1,2]]), CMon(e = 0, num = 104, mult = [ [0,1,2,3,4], [1,2,3,4,0], [2,3,4,0,1], [3,4,0,1,2], [4,0,1,2,3]])] # Computed by Peter Jipsen with SAGE Version 2.1.4 on 2007-04-15 # This file can be used in Python with execfile("filename")