Related papers: Constructions for cyclic sieving phenomena
In this paper, we present examples of the cyclic sieving phenomenon coming from studying independent sets in graphs of a fixed size k. Given a graph G, and a cyclic group C acting on the graph, then C also acts on the collection of…
We prove an instance of the cyclic sieving phenomenon, occurring in the context of noncrossing parititions for well-generated complex reflection groups.
The cyclic sieving phenomenon is a well-studied occurrence in combinatorics appearing when a cyclic group acts on a finite set. In this paper, we demonstrate a natural extension of this theory to finite abelian groups. We also present a…
We exhibit two instances of the cyclic sieving phenomenon - one on dissections of a polygon of a fixed type and one on triangulations of a once-punctured polygon. We use these results to give refined enumerations of certain families of…
We give a $q$-enumeration of circular Dyck paths, which is a superset of the classical Dyck paths enumerated by the Catalan numbers. These objects have recently been studied by Alexandersson and Panova. Furthermore, we show that this…
The cyclic sieving phenomenon (CSP) provides valuable data about symmetry classes of cyclic actions, and has applications to representation theory. In this paper, we enumerate domino tableaux of shape 2-by-n, and use this result to prove a…
Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially $q$-analogues, have useful interpretations related to actions and representations of the cyclic group. We propose a definition of sieving for an…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
We prove cyclic sieving phenomena satisfied by corner-rooted plane trees (alias ordered trees). The sets of rooted plane trees that we consider are: (1) all trees with $n$ nodes; (2) all trees with $n$ nodes and $k$ leaves; (3) all trees…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
We prove an instance of the cyclic sieving phenomenon in non-crossing connected graphs, as conjectured by S.-P. Eu.
We use actions by finite cyclic groups to derive generalizations of three classical theorems from elementary number theory.
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by…
Let Z_m^k consist of the m^k alcoves contained in the m-fold dilation of the fundamental alcove of the type A_k affine hyperplane arrangement. As the fundamental alcove has a cyclic symmetry of order (k+1), so does Z_m^k. By bijectively…
Referring expression comprehension aims to localize objects identified by natural language descriptions. This is a challenging task as it requires understanding of both visual and language domains. One nature is that each object can be…
In this article we give two different ways of representations of circular words. Representations with tuples are intended as a compact notation, while representations with trees give a way to easily process all conjugates of a word. The…
Orbit harmonics is a tool in combinatorial representation theory which promotes the (ungraded) action of a linear group $G$ on a finite set $X$ to a graded action of $G$ on a polynomial ring quotient by viewing $X$ as a $G$-stable point…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…