34 problems

Cyclic sieving conjecture for multi-triangulations. The polynomial $\Omega_{\delta_n}(m;q)$ is a cyclic sieving polynomial for the action of rotation on multi-triangulations. This…

Let $W$ be a finite crystallographic Coxeter group with Coxeter number $h$, let $J(\Phi^+(W))$ be the order ideals of its positive root poset, and let $d_1,d_2,\ldots,d_n$ be the d…

Let $\lambda/\mu$ be a skew shape, let $m$ be a positive integer, and let $k$ be a positive integer. Write $m\lambda/m\mu$ for the skew shape obtained by multiplying every part of…

Bessis's modified-action CSP conjecture. The triple

Let $s$ be a positive integer, let $\Phi$ be a root system of rank $n$ with Coxeter number $h$ and exponents $e_1,\ldots,e_n$, and let $X$ be the set of facets of the generalized c…

Let $W$ be a well-generated finite complex reflection group with degrees $d_1,\dots,d_n$ and Coxeter number $h$, let $d$ be a regular degree, let $W'$ be the centralizer of a $d$-r…

Let $P$ be a finite graded poset of rank $r$ for which the roots of $\aΩ_P(m)$ are all integers or half-integers, and in the latter case possessing an order two automorphism. Let…

Armstrong–Reiner–Rhoades' character conjecture. The character of $\operatorname{PF}$ sends $(c^k,w)$ to

Cyclic sieving conjecture. This conjecture was motivated by the cyclicity of $(\mathbb{Z}/2k\mathbb{Z})^{\times}$ when $k$ is a power of an odd prime. The abstract states that the…

Cyclotomic Catalan conjecture.

Adams et al.'s conjecture. The number of weak excedances that are also mid-points of a decreasing subsequence of length $3$ (Statistic $373$ in FindStat) is equidistributed with th…

Let $n$, $\ell$, and $m$ be integers satisfying … For the bounded-multiplicity Gaussian coefficient $\genfrac{[}{]}{0pt}{}{n}{k}_q^{(n+1)}$, define … The preceding result establish…

Cyclic sieving conjecture. For any positive integer $n$ and $0\leq j\leq n$, the triple

Short-distance inversion conjecture. For $n\geq 2$ even, the number of inversions of distance at most $3$ (Statistic $494$) exhibits the cyclic sieving phenomenon under involutions…

Weak-excedance mid-point conjecture. The number of weak excedances that are also mid-points of a decreasing subsequence of length $3$ (Statistic $373$) is equidistributed with the…

Coxeter-length difference conjecture. The difference in Coxeter length of a permutation and its image under the Simion–Schmidt map (Statistic $123$) exhibits the cyclic sieving phe…

Thomas–Williams' cyclic sieving conjecture. The triple

Dilks–Pechenik–Striker's order conjecture. The order of $K$-promotion on ${\mathrm{Inc}}^q(d^3)$ is exactly $q$.

Propp–Hopkins cyclic sieving conjecture. The triple $(\mathcal{A}^{\ell}(\widetriangle_n),\langle\operatorname*{Row}\rangle,Cat_{\ell}(x))$ exhibits the cyclic sieving phenomenon.

Let $V(n)$ be the poset in the source, let $\mathcal{L}(V(n))$ denote its set of linear extensions, and let $\operatorname{Pro}$ denote promotion. Hopkins–Rubey's conjecture. For e…

Let $\mathfrak g=A_n^{(1)}$, let $\Lambda_0$ be the zeroth fundamental weight, and let $\mx^+(\ell\Lambda_0)$ denote the set of dominant maximal weights of the irreducible highest…

Transpose-and-rowmotion cyclic sieving conjecture. For every $k\in\mathbb Z$,

Let $mathrm{PP}^{m}($ denote the plane partitions of height at most $m$ associate…

Coincidental root-poset cyclic sieving conjecture. For every $\ell\geq 1$, piecewise-linear rowmotion on $\mathrm{PP}^{\ell}(P)$ has order dividing $2h$. If…

Minuscule P-partition cyclic sieving conjecture. For every $\ell\geq 1$, the triple