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{\bf Paul Duncan and Einar Steingr\'imsson}
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{\bf Pattern Avoidance in Ascent Sequences}
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Ascent sequences are sequences of nonnegative integers with
restrictions on the size of each letter, depending on the number of
ascents preceding it in the sequence. Ascent sequences have recently
been related to $(2+2)$-free posets and various other combinatorial
structures. We study pattern avoidance in ascent sequences, giving
several results for patterns of lengths up to 4, for Wilf equivalence
and for growth rates. We establish bijective connections between
pattern avoiding ascent sequences and various other combinatorial
objects, in particular with set partitions. We also make a number of
conjectures related to all of these aspects.
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