The Stein-Lovász Theorem can be used to get existence results for some combinatorial problems using constructive methods rather than probabilistic methods. In this paper, we discuss applications of the Stein-Lovász Theorem to some combinatorial set systems and arrays, including perfect hash families, separating hash families, splitting systems, covering designs, lotto designs and ∆-free systems...

We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain structured cutgenerating functions. This has the consequence of vastly expanding the set of undominated cut generating functions which can be used computationally, compared to known examples from the literature. The result...

For good security and large payload in steganography, it is desired to embed as many messages as possible per change of the coverobject, i.e., to have high embedding efficiency. Steganographic codes derived from covering codes can improve embedding efficiency. In this paper, we propose a new method to construct stego-codes, showing that not just one but a family of stego-codes can be generated ...

We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP. Here, line means a smooth rational curve whose normal bundle is O(1) and the reality implies the invariance under an anti-holomorphic involution on the threefolds. Our threefolds are birational to double covering of CP branched along a singular quartic surface. On these threefolds we find families o...

We consider two broad families of non-additive loss functions covering a large number of applications: rational losses and tropical losses. We give new algorithms extending the Followthe-Perturbed-Leader (FPL) algorithm to both of these families of loss functions and similarly give new algorithms extending the Randomized Weighted Majority (RWM) algorithm to both of these families. We prove that...

Scorpions are one of the most ancient groups of terrestrial animals. They have maintained a steady morphology over more than 400 million years of evolution. Their venom arsenals for capturing prey and defending against predators may play a critical role in their ancient and conservative appearance. In the current review, we present the scorpion fauna of China: 53 species covering five families ...

New constructions of linear nonbinary codes with covering radius R = 2 are proposed. They are in part modifications of earlier constructions by the author and in part are new. Using a starting code with R = 2 as a “seed” these constructions yield an infinite family of codes with the same covering radius. New infinite families of codes with R = 2 are obtained for all alphabets of size q 4 and al...

Simply generated families of trees are described by the equation T (z) = φ(T (z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ {1, . . . , n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are ...

The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints or imposing a particular generating order. In this paper we present generating algorithms and combinatorial Gray codes for several families of pattern avoid...

This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel 1/(1 − θx) in place of the celebrated exponential kernel exp(θx) of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on one side. We illustrate the need for such an extension by showing that cubic pseudo-variance functions correspond to free-i...