I need to construct a regex given an integer n that matches any partition of n with a leading +. For example, if n=10, it should match +10, +9+1, +1+9, +1+8+1 etc.
Since there are only finitely many partitions, I could just list them all. For n=10, this is the result:
\+10|\+9\+1|\+8\+2|\+8\+1\+1|\+7\+3|\+7\+2\+1|\+7\+1\+2|\+7\+1\+1\+1|\+6\+4|\+6\+3\+1|\+6\+2\+2|\+6\+2\+1\+1|\+6\+1\+3|\+6\+1\+2\+1|\+6\+1\+1\+2|\+6\+1\+1\+1\+1|\+5\+5|\+5\+4\+1|\+5\+3\+2|\+5\+3\+1\+1|\+5\+2\+3|\+5\+2\+2\+1|\+5\+2\+1\+2|\+5\+2\+1\+1\+1|\+5\+1\+4|\+5\+1\+3\+1|\+5\+1\+2\+2|\+5\+1\+2\+1\+1|\+5\+1\+1\+3|\+5\+1\+1\+2\+1|\+5\+1\+1\+1\+2|\+5\+1\+1\+1\+1\+1|\+4\+6|\+4\+5\+1|\+4\+4\+2|\+4\+4\+1\+1|\+4\+3\+3|\+4\+3\+2\+1|\+4\+3\+1\+2|\+4\+3\+1\+1\+1|\+4\+2\+4|\+4\+2\+3\+1|\+4\+2\+2\+2|\+4\+2\+2\+1\+1|\+4\+2\+1\+3|\+4\+2\+1\+2\+1|\+4\+2\+1\+1\+2|\+4\+2\+1\+1\+1\+1|\+4\+1\+5|\+4\+1\+4\+1|\+4\+1\+3\+2|\+4\+1\+3\+1\+1|\+4\+1\+2\+3|\+4\+1\+2\+2\+1|\+4\+1\+2\+1\+2|\+4\+1\+2\+1\+1\+1|\+4\+1\+1\+4|\+4\+1\+1\+3\+1|\+4\+1\+1\+2\+2|\+4\+1\+1\+2\+1\+1|\+4\+1\+1\+1\+3|\+4\+1\+1\+1\+2\+1|\+4\+1\+1\+1\+1\+2|\+4\+1\+1\+1\+1\+1\+1|\+3\+7|\+3\+6\+1|\+3\+5\+2|\+3\+5\+1\+1|\+3\+4\+3|\+3\+4\+2\+1|\+3\+4\+1\+2|\+3\+4\+1\+1\+1|\+3\+3\+4|\+3\+3\+3\+1|\+3\+3\+2\+2|\+3\+3\+2\+1\+1|\+3\+3\+1\+3|\+3\+3\+1\+2\+1|\+3\+3\+1\+1\+2|\+3\+3\+1\+1\+1\+1|\+3\+2\+5|\+3\+2\+4\+1|\+3\+2\+3\+2|\+3\+2\+3\+1\+1|\+3\+2\+2\+3|\+3\+2\+2\+2\+1|\+3\+2\+2\+1\+2|\+3\+2\+2\+1\+1\+1|\+3\+2\+1\+4|\+3\+2\+1\+3\+1|\+3\+2\+1\+2\+2|\+3\+2\+1\+2\+1\+1|\+3\+2\+1\+1\+3|\+3\+2\+1\+1\+2\+1|\+3\+2\+1\+1\+1\+2|\+3\+2\+1\+1\+1\+1\+1|\+3\+1\+6|\+3\+1\+5\+1|\+3\+1\+4\+2|\+3\+1\+4\+1\+1|\+3\+1\+3\+3|\+3\+1\+3\+2\+1|\+3\+1\+3\+1\+2|\+3\+1\+3\+1\+1\+1|\+3\+1\+2\+4|\+3\+1\+2\+3\+1|\+3\+1\+2\+2\+2|\+3\+1\+2\+2\+1\+1|\+3\+1\+2\+1\+3|\+3\+1\+2\+1\+2\+1|\+3\+1\+2\+1\+1\+2|\+3\+1\+2\+1\+1\+1\+1|\+3\+1\+1\+5|\+3\+1\+1\+4\+1|\+3\+1\+1\+3\+2|\+3\+1\+1\+3\+1\+1|\+3\+1\+1\+2\+3|\+3\+1\+1\+2\+2\+1|\+3\+1\+1\+2\+1\+2|\+3\+1\+1\+2\+1\+1\+1|\+3\+1\+1\+1\+4|\+3\+1\+1\+1\+3\+1|\+3\+1\+1\+1\+2\+2|\+3\+1\+1\+1\+2\+1\+1|\+3\+1\+1\+1\+1\+3|\+3\+1\+1\+1\+1\+2\+1|\+3\+1\+1\+1\+1\+1\+2|\+3\+1\+1\+1\+1\+1\+1\+1|\+2\+8|\+2\+7\+1|\+2\+6\+2|\+2\+6\+1\+1|\+2\+5\+3|\+2\+5\+2\+1|\+2\+5\+1\+2|\+2\+5\+1\+1\+1|\+2\+4\+4|\+2\+4\+3\+1|\+2\+4\+2\+2|\+2\+4\+2\+1\+1|\+2\+4\+1\+3|\+2\+4\+1\+2\+1|\+2\+4\+1\+1\+2|\+2\+4\+1\+1\+1\+1|\+2\+3\+5|\+2\+3\+4\+1|\+2\+3\+3\+2|\+2\+3\+3\+1\+1|\+2\+3\+2\+3|\+2\+3\+2\+2\+1|\+2\+3\+2\+1\+2|\+2\+3\+2\+1\+1\+1|\+2\+3\+1\+4|\+2\+3\+1\+3\+1|\+2\+3\+1\+2\+2|\+2\+3\+1\+2\+1\+1|\+2\+3\+1\+1\+3|\+2\+3\+1\+1\+2\+1|\+2\+3\+1\+1\+1\+2|\+2\+3\+1\+1\+1\+1\+1|\+2\+2\+6|\+2\+2\+5\+1|\+2\+2\+4\+2|\+2\+2\+4\+1\+1|\+2\+2\+3\+3|\+2\+2\+3\+2\+1|\+2\+2\+3\+1\+2|\+2\+2\+3\+1\+1\+1|\+2\+2\+2\+4|\+2\+2\+2\+3\+1|\+2\+2\+2\+2\+2|\+2\+2\+2\+2\+1\+1|\+2\+2\+2\+1\+3|\+2\+2\+2\+1\+2\+1|\+2\+2\+2\+1\+1\+2|\+2\+2\+2\+1\+1\+1\+1|\+2\+2\+1\+5|\+2\+2\+1\+4\+1|\+2\+2\+1\+3\+2|\+2\+2\+1\+3\+1\+1|\+2\+2\+1\+2\+3|\+2\+2\+1\+2\+2\+1|\+2\+2\+1\+2\+1\+2|\+2\+2\+1\+2\+1\+1\+1|\+2\+2\+1\+1\+4|\+2\+2\+1\+1\+3\+1|\+2\+2\+1\+1\+2\+2|\+2\+2\+1\+1\+2\+1\+1|\+2\+2\+1\+1\+1\+3|\+2\+2\+1\+1\+1\+2\+1|\+2\+2\+1\+1\+1\+1\+2|\+2\+2\+1\+1\+1\+1\+1\+1|\+2\+1\+7|\+2\+1\+6\+1|\+2\+1\+5\+2|\+2\+1\+5\+1\+1|\+2\+1\+4\+3|\+2\+1\+4\+2\+1|\+2\+1\+4\+1\+2|\+2\+1\+4\+1\+1\+1|\+2\+1\+3\+4|\+2\+1\+3\+3\+1|\+2\+1\+3\+2\+2|\+2\+1\+3\+2\+1\+1|\+2\+1\+3\+1\+3|\+2\+1\+3\+1\+2\+1|\+2\+1\+3\+1\+1\+2|\+2\+1\+3\+1\+1\+1\+1|\+2\+1\+2\+5|\+2\+1\+2\+4\+1|\+2\+1\+2\+3\+2|\+2\+1\+2\+3\+1\+1|\+2\+1\+2\+2\+3|\+2\+1\+2\+2\+2\+1|\+2\+1\+2\+2\+1\+2|\+2\+1\+2\+2\+1\+1\+1|\+2\+1\+2\+1\+4|\+2\+1\+2\+1\+3\+1|\+2\+1\+2\+1\+2\+2|\+2\+1\+2\+1\+2\+1\+1|\+2\+1\+2\+1\+1\+3|\+2\+1\+2\+1\+1\+2\+1|\+2\+1\+2\+1\+1\+1\+2|\+2\+1\+2\+1\+1\+1\+1\+1|\+2\+1\+1\+6|\+2\+1\+1\+5\+1|\+2\+1\+1\+4\+2|\+2\+1\+1\+4\+1\+1|\+2\+1\+1\+3\+3|\+2\+1\+1\+3\+2\+1|\+2\+1\+1\+3\+1\+2|\+2\+1\+1\+3\+1\+1\+1|\+2\+1\+1\+2\+4|\+2\+1\+1\+2\+3\+1|\+2\+1\+1\+2\+2\+2|\+2\+1\+1\+2\+2\+1\+1|\+2\+1\+1\+2\+1\+3|\+2\+1\+1\+2\+1\+2\+1|\+2\+1\+1\+2\+1\+1\+2|\+2\+1\+1\+2\+1\+1\+1\+1|\+2\+1\+1\+1\+5|\+2\+1\+1\+1\+4\+1|\+2\+1\+1\+1\+3\+2|\+2\+1\+1\+1\+3\+1\+1|\+2\+1\+1\+1\+2\+3|\+2\+1\+1\+1\+2\+2\+1|\+2\+1\+1\+1\+2\+1\+2|\+2\+1\+1\+1\+2\+1\+1\+1|\+2\+1\+1\+1\+1\+4|\+2\+1\+1\+1\+1\+3\+1|\+2\+1\+1\+1\+1\+2\+2|\+2\+1\+1\+1\+1\+2\+1\+1|\+2\+1\+1\+1\+1\+1\+3|\+2\+1\+1\+1\+1\+1\+2\+1|\+2\+1\+1\+1\+1\+1\+1\+2|\+2\+1\+1\+1\+1\+1\+1\+1\+1|\+1\+9|\+1\+8\+1|\+1\+7\+2|\+1\+7\+1\+1|\+1\+6\+3|\+1\+6\+2\+1|\+1\+6\+1\+2|\+1\+6\+1\+1\+1|\+1\+5\+4|\+1\+5\+3\+1|\+1\+5\+2\+2|\+1\+5\+2\+1\+1|\+1\+5\+1\+3|\+1\+5\+1\+2\+1|\+1\+5\+1\+1\+2|\+1\+5\+1\+1\+1\+1|\+1\+4\+5|\+1\+4\+4\+1|\+1\+4\+3\+2|\+1\+4\+3\+1\+1|\+1\+4\+2\+3|\+1\+4\+2\+2\+1|\+1\+4\+2\+1\+2|\+1\+4\+2\+1\+1\+1|\+1\+4\+1\+4|\+1\+4\+1\+3\+1|\+1\+4\+1\+2\+2|\+1\+4\+1\+2\+1\+1|\+1\+4\+1\+1\+3|\+1\+4\+1\+1\+2\+1|\+1\+4\+1\+1\+1\+2|\+1\+4\+1\+1\+1\+1\+1|\+1\+3\+6|\+1\+3\+5\+1|\+1\+3\+4\+2|\+1\+3\+4\+1\+1|\+1\+3\+3\+3|\+1\+3\+3\+2\+1|\+1\+3\+3\+1\+2|\+1\+3\+3\+1\+1\+1|\+1\+3\+2\+4|\+1\+3\+2\+3\+1|\+1\+3\+2\+2\+2|\+1\+3\+2\+2\+1\+1|\+1\+3\+2\+1\+3|\+1\+3\+2\+1\+2\+1|\+1\+3\+2\+1\+1\+2|\+1\+3\+2\+1\+1\+1\+1|\+1\+3\+1\+5|\+1\+3\+1\+4\+1|\+1\+3\+1\+3\+2|\+1\+3\+1\+3\+1\+1|\+1\+3\+1\+2\+3|\+1\+3\+1\+2\+2\+1|\+1\+3\+1\+2\+1\+2|\+1\+3\+1\+2\+1\+1\+1|\+1\+3\+1\+1\+4|\+1\+3\+1\+1\+3\+1|\+1\+3\+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This is 8960 characters long. A shorter version is
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This is 2561 characters long.
For obvious reasons, both of these aren't very good solutions. Is there a smarter way to do this?
Sorry if this has been answered before, this doesn't lend itself to Googling very easily.