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ParallelMapMonitored[{#,Length[EnumerateSubstitutionSystemRules[#,2]]}&,{{11},{12},{13},{22},{23},{24},{33},{11,11},{12,11},{13,11},{12,12},{12,21},{13,31},{12,22},{13,22},{12,33},{11,11,11},{12,11,11}}]
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Grid[%,FrameAll]
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ParallelMapMonitored[{#,Length[EnumerateSubstitutionSystemRules[#,3]]}&,{{11},{12},{13},{22},{23},{24},{33},{11,11},{12,11},{13,11},{12,21},{13,31},{12,22},{13,22},{12,33}}]
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EnumerateSubstitutionSystemRules[{11,11},2]
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{{AA,AA},{AA,AB},{AA,BA},{AA,BB},{AB,AA},{AB,AB},{AB,BA},{AB,BB}}
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(Rule@@@Partition[#,2])&/@Catenate[Permutations@*Reverse/@Select[IntegerPartitions[5],EvenQ@*Length]]
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{{14},{41},{23},{32},{11,12},{11,21},{12,11},{21,11}}
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(Rule@@@Partition[#,2])&/@Catenate[Permutations@*Reverse/@Select[IntegerPartitions[2],EvenQ@*Length]]
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{{11}}
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(Rule@@@Partition[#,2])&/@Catenate[Permutations@*Reverse/@Select[IntegerPartitions[3],EvenQ@*Length]]
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{{12},{21}}
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(Rule@@@Partition[#,2])&/@Catenate[Permutations@*Reverse/@Select[IntegerPartitions[4],EvenQ@*Length]]
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{{13},{31},{22},{11,11}}
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DeleteDuplicatesBy[(Rule@@@Partition[#,2])&/@Catenate[Permutations@*Reverse/@Select[IntegerPartitions[5],EvenQ@*Length]],Sort]
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{{14},{41},{23},{32},{11,12},{11,21}}
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DeleteDuplicatesBy[(Rule@@@Partition[#,2])&/@Catenate[Permutations@*Reverse/@Select[IntegerPartitions[6],EvenQ@*Length]],Sort]
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{{15},{51},{24},{42},{33},{11,13},{11,31},{11,22},{12,12},{12,21},{21,21},{11,11,11}}
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Catenate[Table[(Rule@@@Partition[#,2])&/@Catenate[Permutations@*Reverse/@Select[IntegerPartitions[n],EvenQ@*Length]],{n,8}]]
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Select[%,SomeIncreasingQ]
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SomeIncreasingQ[list_]:=AnyTrue[#2-#1&@@@list,Positive]||AllTrue[#2-#1&@@@list,#0&]
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#2-#1&@@@{21,11,11}
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{-1,0,0}
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allsigs
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ParallelMapMonitored[{#,Length[EnumerateSubstitutionSystemRules[#,2]]}&,allsigs]
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Divisors[48]
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{1,2,3,4,6,8,12,16,24,48}