Related papers: On rearrangement inequalities for multiple sequenc…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
The classical AM-GM inequality has been generalized in a number of ways. Generalizations which incorporate variance appear to be the most useful in economics and finance, as well as mathematically natural. Previous work leaves unanswered…
The aims of this paper are twofold. First, it discusses the Littlewood conjecture and its variants with respect to uniformly distributed sequences. The second aim is to determine the exact order of the discrepancy of the van der…
A common issue for classification in scientific research and industry is the existence of imbalanced classes. When sample sizes of different classes are imbalanced in training data, naively implementing a classification method often leads…
The poset of permutations of [n] under Bruhat ordering is studied. We give nontrivial upper and lower bounds for the number of comparable pairs of permutations in both the weak and strong versions of this order. In light of numerical…
We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive…
We present a new elementary proof of the existence of the least and the greatest solutions to initial value problems in the conditions of Peano's existence theorem. Our proof is based on a modification of Perron's method which allows us to…
We are interested in solutions of a norm form equation that takes values in a given multi-recurrence. We show that among the solutions there are only finitely many values in each component which lie in the given multi-recurrence unless the…
In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is the following: at each stage, a designated agent picks one object among those that…
Talenti inequalities are a central feature in the qualitative analysis of PDE constrained optimal control as well as in calculus of variations. The classical parabolic Talenti inequality states that if we consider the parabolic equation…
Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…
This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…
In queueing theory, Lorden's inequality can be used for bounds estimation of the moments of backward and forward renewal times. Two random variables called backwards renewal time and forward renewal time for this process are defined.…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
In a multiple-object auction, every bidder tries to win as many objects as possible with a bidding algorithm. This paper studies position-randomized auctions, which form a special class of multiple-object auctions where a bidding algorithm…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected…
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.