相关论文: A poset-like approach to positive opetopes
A residuated poset is a structure $\langle A,\le,\cdot,\backslash,/,1 \rangle$ where $\langle A,\le \rangle$ is a poset and $\langle A,\cdot,1 \rangle$ is a monoid such that the residuation law $x\cdot y\le z\iff x\le z/y\iff y\le…
We survey all known examples of finite posets whose order polynomials have product formulas, and we propose the heuristic that these are the same posets with good dynamical behavior. Here the dynamics in question are the actions of…
We present a method to compute integral cohomology of posets. This toolbox is applicable as soon as the sub-posets under each object possess certain structure. This is the case for simplicial complexes and simplex-like posets. The method is…
A stratified space is a topological space equipped with a \emph{stratification}, which is a decomposition or partition of the topological space satisfying certain extra conditions. More recently, the notion of poset-stratified space, i.e.,…
In this article we study different aspects of Hermitian operators applying the concept of positive decompositions. On the one hand, we characterize the positivity of an Hermitian operator by means of a norm condition where the factors of…
We provide new structural results on sets of positive reach in Euclidean spaces and Riemannian manifolds.
Inspired by Zhao and Xu's study on which a dcpo can be determined by its Scott closed subsets lattice, we further investigate whether a poset (or dcpo) $P$ is able to be determined by the family $\mathcal Q(P)$ of its Scott compact…
We show that all totally positive formal power series with integer coefficients and constant term $1$ are precisely the rank-generating functions of Schur-positive upho posets, thereby resolving the main conjecture proposed by Gao, Guo,…
We propose an end-to-end trainable approach for multi-instance pose estimation, called POET (POse Estimation Transformer). Combining a convolutional neural network with a transformer encoder-decoder architecture, we formulate multiinstance…
While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the…
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…
Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
The faces of a convex set owe their relevance to an interplay between convexity and topology that is systematically studied in the work of Rockafellar. Infinite-dimensional convex sets are excluded from this theory as their relative…
We introduce a construction called realisation which transforms posets into posets. We show that realisations share several key features with upper semilattices. For example, we define local dimensions of points in a poset and show that…
In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group $G$, induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of $G$. We prove that in several…
We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…
We show that the category of principal ordered face structures is equivalent to the category of multitopes. We show that the category of principal ordered face structures is equivalent to the category of multitopes. On the way we introduce…
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…
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…