This book gives an introduction to and an overview of the methods used in the combinatorics
of pattern avoidance and pattern enumeration in set partitions, a very active area of research …

We present an equivariant bijection between two actions—promotion and rowmotion—on
order ideals in certain posets. This bijection simultaneously generalizes a result of R …

Many invertible actions $\tau $ on a set $\mathcal {S} $ of combinatorial objects, along with a
natural statistic $ f $ on $\mathcal {S} $, exhibit the following property which we dub …

Rowmotion is a simple cyclic action on the distributive lattice of order ideals of a poset: it
sends the order ideal x to the order ideal generated by the minimal elements not in x. It can …

We survey recent work within the area of algebraic combinatorics that has the flavor of
discrete dynamical systems, with a particular focus on the homomesy phenomenon codified …

Birational rowmotion—a birational map associated to any finite poset P—has been
introduced by Einstein and Propp as a far-reaching generalization of the (well-studied) …

We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family
of rational noncrossing objects for any finite Coxeter group, using the combinatorics of …

The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper.
Let X be a finite set, C be a finite cyclic group acting on X, and f (q) be a polynomial in q with …

We introduce a new concept of resonance on discrete dynamical systems. This concept
formalizes the observation that, in various combinatorially-natural cyclic group actions, orbit …

arXiv:1803.06636v2 [math.CO] 31 Mar 2018 Page 1 arXiv:1803.06636v2 [math.CO] 31 Mar
2018 COMPLEXITY PROBLEMS IN ENUMERATIVE COMBINATORICS IGOR PAK⋆ Abstract …