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In their study of the densest jammed configurations for theater models, Krapivsky and Luck observe that two classes of permutations have the same cardinalities and ask for a bijection between them. In this note we show that the Foata correspondence provides the desired bijection.
Woodall proved that for a graph $G$ of order $ngeq 2k+3$ where $kgeq 0$ is an integer, if $e(G)geq binom{n-k-1}{2}+binom{k+2}{2}+1$ then $G$ contains a $C_{ell}$ for each $ellin [3,n-k]$. In this article, we prove a stability result of this theorem.
Visual semantic correspondence is an important topic in computer vision and could help machine understand objects in our daily life. However, most previous methods directly train on correspondences in 2D images, which is end-to-end but loses plenty o
Image co-segmentation is an active computer vision task that aims to segment the common objects from a set of images. Recently, researchers design various learning-based algorithms to undertake the co-segmentation task. The main difficulty in this ta
A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al., where 25 out of 65 non-equivalent cases were solved. In this paper, we give 27 distribution results for these patterns including 14 distributions for whi
Necessary and sufficient conditions are derived for a social choice correspondence to be the one that selects the Pareto optimal alternatives.