Séminaire Lotharingien de Combinatoire, B81d (2020), 21 pp.
Henri Mühle, Philippe Nadeau and Nathan Williams
k-Indivisible Noncrossing Partitions
Abstract.
For a fixed integer k, we consider the set of noncrossing
partitions, where both the block sizes and the difference between
adjacent elements in a block is 1 (mod k). We show that these
k-indivisible noncrossing partitions can be recovered in
the setting of subgroups of the symmetric group generated by
(k+1)-cycles, and that the poset of k-indivisible noncrossing
partitions under refinement order has many beautiful enumerative and
structural properties. We encounter k-parking functions and some
special Cambrian lattices on the way, and show that a special class
of lattice paths constitutes a nonnesting analogue.
Received: April 9, 2019.
Accepted: October 5, 2019.
Final Version: March ??, 2020.
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