Séminaire Lotharingien de Combinatoire, 91B.53 (2024), 12 pp.
Matthew Plante and Tom Roby
I>Whirling and Rowmotion Dynamics on The Chain of V's Poset
Abstract.
Given a finite poset P, we study the whirling action on
vertex-labelings of P
with the elements {0,1,2,...,k}. When such labelings are
(weakly) order-reversing,
we call them k-bounded P-partitions.
We give a general equivariant bijection
between k-bounded P-partitions and order
ideals of the poset P × [k] which conveys whirling to the
well-studied rowmotion operator. As an
application, we derive periodicity and homomesy results for rowmotion acting on
the chain of V's poset V × [k]. We are able to
generalize some of these results to
the more complicated dynamics of rowmotion on Cn × [k],
where Cn is the
claw poset with n unrelated elements each covering
0^.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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