16 citations · 16 across the 4 of their papers we have counts for
5 papers · 1 filter
Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks
Sam Hopkins, Jesse Kim, Stephan Pfannerer
We prove a cyclic sieving result for the action of promotion on the staircase plane partitions of height two. Our proof has two major algebraic inputs: an interpretation of this pr…
Two -analogues of the tree inversion enumerator
Sam Hopkins
In this note, we introduce two -analogues and of the tree inversion enumerator . Although similar, and $\widetilde{I}_n(q,t)…
Upho lattices II: ways of realizing a core
Sam Hopkins, Joel B. Lewis
A poset is called upper homogeneous, or "upho," if all of its principal order filters are isomorphic to the whole poset. In previous work of the first author, it was shown that eac…
Upho lattices I: examples and non-examples of cores
Sam Hopkins
A poset is called upper homogeneous, or "upho," if every principal order filter of the poset is isomorphic to the whole poset. We study (finite type -graded) upho latti…
Cyclic Sieving for Plane Partitions and Symmetry
Sam Hopkins
The cyclic sieving phenomenon of Reiner, Stanton, and White says that we can often count the fixed points of elements of a cyclic group acting on a combinatorial set by plugging ro…