Related papers: Geometric Symmetric Chain Decompositions
We introduce posets with interfaces (iposets) and generalise their standard serial composition to a new gluing composition. In the partial order semantics of concurrency, interfaces and gluing allow modelling events that extend in time and…
Breaking symmetries is a popular way of speeding up the branch-and-bound method for symmetric integer programs. We study fundamental domains, which are minimal and closed symmetry breaking polyhedra. Our long-term goal is to understand the…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
We extend the notion of chain algebra, originally defined in \cite{GN} for finite distributive lattices, to that of finite pure posets. We show this algebra corresponds to the Ehrhart ring of a (0,1)-polytope, termed the chain polytope, and…
We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high…
Learning methods for relative camera pose estimation have been developed largely in isolation from classical geometric approaches. The question of how to integrate predictions from deep neural networks (DNNs) and solutions from geometric…
We discuss recent developments in the study of semiorthogonal decompositions of algebraic varieties with an emphasis on their behaviour in families. First, we overview new results concerning homological projective duality. Then we introduce…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
This paper introduces a novel $k$-cell decomposition method for pursuit-evasion problems in polygonal environments, where a searcher is equipped with a $k$-modem: a device capable of seeing through up to $k$ walls. The proposed…
In certain finite posets, the expected down-degree of their elements is the same whether computed with respect to either the uniform distribution or the distribution weighting an element by the number of maximal chains passing through it.…
This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams,…
The fusion procedure provides a way to construct new solutions to the Yang-Baxter equation. In the case of the symmetric group the fusion procedure has been used to construct diagonal matrix elements using a decomposition of the Young…
Spatial perception aims to estimate camera motion and scene structure from visual observations, a problem traditionally addressed through geometric modeling and physical consistency constraints. Recent learning-based methods have…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
In a recent study by Tenner, the concept of the interval poset of a permutation was introduced to effectively represent all intervals and their inclusions within a permutation. In this paper, we present a new geometric viewpoint on interval…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
Shape assembly, which aims to reassemble separate parts into a complete object, has gained significant interest in recent years. Existing methods primarily rely on networks to predict the poses of individual parts, but often fail to…
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
Motivated by the classical type decomposition of von Neumann algebras, and various more recent extensions to other structures, we develop a type decomposition theory for general posets.