Lower bounds of 4, 3, and 8 additional relations for T_n, I_n, PT_n beyond the symmetric group, with matching explicit presentations for n large enough.
Braids and partial permutations
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Short presentations for transformation monoids
Lower bounds of 4, 3, and 8 additional relations for T_n, I_n, PT_n beyond the symmetric group, with matching explicit presentations for n large enough.