Related papers: Crystal skeletons: Combinatorics and axioms
Combining skeleton structure with graph convolutional networks has achieved remarkable performance in human action recognition. Since current research focuses on designing basic graph for representing skeleton data, these embedding features…
We show that the metric structure of morphisms $f\colon Y\to X$ between quasi-smooth compact Berkovich curves over an algebraically closed field admits a finite combinatorial description. In particular, for a large enough skeleton…
We introduce coplactic raising and lowering operators $E'_i$, $F'_i$, $E_i$, and $F_i$ on shifted skew semistandard tableaux. We show that the primed operators and unprimed operators each independently form type A Kashiwara crystals (but…
We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge…
A structure model of atoms of two sizes, interacting with Lennard-Jones potentials and simulated by molecular dynamics, was observed to freeze into a decagonal quasicrystal dominated by Frank-Kasper coordination shells and closely related…
We introduce a type $A$ crystal structure on decreasing factorizations of fully-commutative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing…
We continue work begun in \cite{ptab} which introduced \emph{perforated tableaux} as a combinatorial model for crystals of type $A_{n-1}$, emphasizing connections to the classical Robinson-Schensted-Knuth (RSK) correspondence and Lusztig…
Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant…
Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid.…
Crystallographic groups are conventionally studied in real space to characterize crystal symmetries. Recent work has recognized that when these symmetries are realized projectively, momentum space inherently accommodates nonsymmorphic…
This mostly expository article explores recent developments in the relations between the three objects in the title from an algebro-combinatorial perspective. We prove a formula for Whittaker functions of a real semisimple group as an…
We describe the upper seminormal crystal structure for the $\mu$-supported $\delta$-vectors for any quiver with potential with reachable frozen vertices, or equivalently for the tropical points of the corresponding cluster $\mc{X}$-variety.…
Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional…
This paper introduces a notion of presentation for locally inverse semigroups and develops a graph structure to describe the elements of locally inverse semigroups given by these presentations. These graphs will have a role similar to the…
What might a combinatorial interpretation of the Kronecker coefficients even look like? We introduce a class of combinatorial objects called bitableaux, which we believe are a natural candidate, and we formulate a purely combinatorial…
The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we…
Through extensive molecular simulations we determine a phase diagram of attractive, flexible polymer chains in two and three dimensions. A surprisingly rich collection of distinct crystal morphologies appear, which can be finely tuned…
Crystal structure prediction is a long-standing challenge in materials science, with most data-driven methods developed for inorganic systems. This leaves an important gap for organic crystals, which are central to pharmaceuticals,…
A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain…
The physics of nematic liquid crystals has been subject of intensive research since the late 19th century. However, because of the limitations of chemistry the focus has been centered around uni- and biaxial nematics associated with…