Related papers: Face numbers of down-sets

The paper addresses an approach to ordinal assessment of alternatives based on assignment of elements into an ordinal scale. Basic versions of the assessment problems are formulated while taking into account the number of levels at a basic…

The limited capacity to recognize faces under occlusions is a long-standing problem that presents a unique challenge for face recognition systems and even for humans. The problem regarding occlusion is less covered by research when compared…

This paper presents a part-based face detection approach where the spatial relationship between the face parts is represented by a hidden 3D model with six parameters. The computational complexity of the search in the six dimensional pose…

A triangulation of a simplicial complex $\Delta$ is called uniform if the $f$-vector of its restriction to a face of $\Delta$ depends only on the dimension of that face. This paper proves that the entries of the $h$-vector of a uniform…

A general proposition is proved relating multiplicities (of restriction of a representation of a group to a subgroup) under basechange, and used to calculate some multiplicities for cuspidal representations which become principal series…

In [Baumeister, H., Nill, Paffenholz, On permutation polytopes, Adv. Math. 222 (2009), 431-452 / arXiv:0709.1615] we conjectured a characterization of subgroups H of a permutation group G so that, on the level of permutation polytopes, P(H)…

A typical goal of research in combinatorial optimization is to come up with fast algorithms that find optimal solutions to a computational problem. The process that takes a real-world problem and extracts a clean mathematical abstraction of…

Open-set face recognition describes a scenario where unknown subjects, unseen during the training stage, appear on test time. Not only it requires methods that accurately identify individuals of interest, but also demands approaches that…

We extend the definition of an orbit portrait to the context of non-autonomous iteration, both for the combinatorial version involving collections of angles and for the dynamic version involving external rays where combinatorial portraits…

In this note, working in the context of simplicial sets, we give a detailed study of the complexity for computing chain level Steenrod squares, in terms of the number of face operators required. This analysis is based on the combinatorial…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and eight combinatorial identities involving…

We consider closed simplicial and cubical $n$-complexes in terms of link of their $(n-2)$-faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every $(n-2)$-face is contained in 3 or 4 $n$-faces. Such simplicial…

Recognizing a face based on its attributes is an easy task for a human to perform as it is a cognitive process. In recent years, Face Recognition is achieved with different kinds of facial features which were used separately or in a…

We study efficient combinatorial algorithms to produce the Hasse diagram of the poset of bounded faces of an unbounded polyhedron, given vertex-facet incidences. We also discuss the special case of simple polyhedra and present computational…

When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…

Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits…

Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional…

We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope. We use this correspondence to prove combinatorial results…

In this paper we introduce and study a new family of combinatorial simplicial complexes, which we call immediate snapshot complexes. Our construction and terminology is strongly motivated by theoretical distributed computing, as these…