Related papers: Face numbers of down-sets
We establish results about algebraic shifting of simplicial complexes and use them to compare different shifting operations. In particular, we show that each shifting operation does not decrease the number of facets, and that the exterior…
We introduce a new combinatorial invariant, which we call crosscut poset, that is finer than the crosscut complex. We exhibit many applications of the crosscut poset which include a generalization of Bj\"orner's crosscut theorem and two…
In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…
Facial attribute analysis in the real world scenario is very challenging mainly because of complex face variations. Existing works of analyzing face attributes are mostly based on the cropped and aligned face images. However, this result in…
This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.
In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing…
This paper presents Hierarchical Network Dissection, a general pipeline to interpret the internal representation of face-centric inference models. Using a probabilistic formulation, our pipeline pairs units of the model with concepts in our…
Face detection is a crucial first step in many facial recognition and face analysis systems. Early approaches for face detection were mainly based on classifiers built on top of hand-crafted features extracted from local image regions, such…
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we…
We introduce poly-Cauchy permutations that are enumerated by the poly-Cauchy numbers. We provide combinatorial proofs for several identities involving poly-Cauchy numbers and some of their generalizations. The aim of this work is to…
In the recent past, different researchers have proposed privacy-enhancing face recognition systems designed to conceal soft-biometric attributes at feature level. These works have reported impressive results, but generally did not consider…
This paper develops asymptotic methods to count faces of random high-dimensional polytopes. Beyond its intrinsic interest, our conclusions have surprising implications - in statistics, probability, information theory, and signal processing…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
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 describe recent advances in the study of random analogues of combinatorial theorems.
Several methods for inversion of face recognition models were recently presented, attempting to reconstruct a face from deep templates. Although some of these approaches work in a black-box setup using only face embeddings, usually, on the…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
We discuss the combinatorics of faces of trees in the context of dendroidal sets and develop a systematic treatment of dendroidal anodyne extensions. As the main example and our motivation, we prove the pushout-product property for the…