Related papers: Geometric view of interval poset permutations
In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these…
We study three different poset structures on the set of all compositions. In the first case, the covering relation consists of inserting a part of size one to the left or to the right, or increasing the size of some part by one. The…
Two axioms of order geoemtry are the poset axioms of transitivity and antisymmetry of the relation "is in front of" when looking from a point. From these axioms, by looking from an interval instead of a point, further well-known axioms of…
We continue the study of intersection bodies of polytopes, focusing on the behavior of $IP$ under translations of $P$. We introduce an affine hyperplane arrangement and show that the polynomials describing the boundary of $I(P+t)$ can be…
This is a study of the construction of particular regular sub-n-gons T in regular n-gons P using a special system of chords of P. In particular, some of these sub-n-gons have areas which are integer divisors of the area of the given n-gon…
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…
We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio…
In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.
Dimension is a standard and well-studied measure of complexity of posets. Recent research has provided many new upper bounds on the dimension for various structurally restricted classes of posets. Bounded dimension gives a succinct…
The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by…
Several recent papers have examined a rational polyhedron $P_m$ whose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containing $m$. A combinatorial…
We study the approximability of general convex sets in $\mathbb{R}^n$ by intersections of halfspaces, where the approximation quality is measured with respect to the standard Gaussian distribution $N(0,I_n)$ and the complexity of an…
We review the notion of shape tensor of an embedded manifold, which efficiently combines intrinsic and extrinsic geometry, and allows for intuitive understanding of some basic concepts of classical differential geometry, such as parallel…
This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…
We introduce two partially ordered sets, $P^A_n$ and $P^B_n$, of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of $P^A_n$ and $P^B_n$ are subsets of the symmetric and the hyperoctahedral…
In this work, we focus on the task of learning and representing dense correspondences in deformable object categories. While this problem has been considered before, solutions so far have been rather ad-hoc for specific object types (i.e.,…
Pairwise pose estimation from images with little or no overlap is an open challenge in computer vision. Existing methods, even those trained on large-scale datasets, struggle in these scenarios due to the lack of identifiable…
We compare a traditional and non-traditional view on the subject of P-partitions, leading to formulas counting linear extensions of certain posets.
A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat (2019) and the Polymath REU (2020), continues to investigate representations of convex geometries with small…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…