Nine classes of pattern-avoiding uniquely sorted permutations are enumerated via bijections with Dyck, S-Motzkin, and Schröder paths, confirming Defant's conjectures.
Stack words and a bound for 3-stack sortable permutations
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abstract
We use stack words to find a new, simple proof for the best known upper bound for the number of 3-stack sortable permutations of a given length. This is the first time that stack words are used to obtain such a result.
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math.CO 1years
2019 1verdicts
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Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
Nine classes of pattern-avoiding uniquely sorted permutations are enumerated via bijections with Dyck, S-Motzkin, and Schröder paths, confirming Defant's conjectures.