Geodesic
k-Indivisible Noncrossing Partitions
Séminaire lotharingien de combinatoire, Tome 81 (2020)

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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. 

@article{SLC_2020_81_a3,
     author = {Henri M\"uhle and Philippe Nadeau and Nathan Williams},
     title = {k-Indivisible {Noncrossing} {Partitions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {81},
     year = {2020},
     url = {http://geodesic.mathdoc.fr/item/SLC_2020_81_a3/}
}
TY  - JOUR
AU  - Henri Mühle
AU  - Philippe Nadeau
AU  - Nathan Williams
TI  - k-Indivisible Noncrossing Partitions
JO  - Séminaire lotharingien de combinatoire
PY  - 2020
VL  - 81
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2020_81_a3/
ID  - SLC_2020_81_a3
ER  - 
%0 Journal Article
%A Henri Mühle
%A Philippe Nadeau
%A Nathan Williams
%T k-Indivisible Noncrossing Partitions
%J Séminaire lotharingien de combinatoire
%D 2020
%V 81
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2020_81_a3/
%F SLC_2020_81_a3
Henri Mühle; Philippe Nadeau; Nathan Williams. k-Indivisible Noncrossing Partitions. Séminaire lotharingien de combinatoire, Tome 81 (2020). http://geodesic.mathdoc.fr/item/SLC_2020_81_a3/