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In this note, we prove some and conjecture other results regarding thedistribution of descent top and descent bottom sets on some pattern-avoidingpermutations. In particular, for 3-letter patterns, we show bijectively thatthe set of descent tops and the set of descent bottoms are jointlyequidistributed on the avoiders of 231 and 312. We also conjecture similarequidistributions for 4-letter patterns, in particular, that the set of descenttops and the set of descent bottoms are jointly equidistributed on the avoidersof 3142, 3241, 4132.

Distribution of sets of descent tops and descent bottoms on restricted permutations