SimionSchmidtPreimageSize on Permutation
The permutations sent to p by the Simion-Schmidt map onto the 321-avoiding permutations.
That map keeps the left-to-right maxima and puts the other entries in increasing order, so p needs those increasing; each other position then chooses among the smaller values left.
Called as CombinatorialStat(x, "SimionSchmidtPreimageSize"). The head's page has its examples.
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FindStat St000124
The cardinality of the preimage of the Simion-Schmidt map.
| Object | Value |
|---|---|
[1] | 1 |
[1,2] | 1 |
[2,1] | 1 |
[1,2,3] | 1 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 1 |
[3,1,2] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000124 has the rest.