We consider the following q-analog of the basic combinatorial search problem: let q be a prime power and GF(q) the finite field of q elements. Let V denote an n-dimensional vector space over GF(q) and let v be an unknown 1-dimensional subspace of V . We will be interested in determining the minimum number of queries that is needed to find v provided all queries are subspaces of V and the answer...

Bus network design is an important problem in public transportation. A main step to this design is determining the number of required terminals and their locations. This is a special type of facility location problem, which is a time-consuming, large scale, combinatorial problem. In a previous attempt by the authors, this problem had been solved by GAMS, based on a branch and bound algorithm.&...

In this thesis we consider a three-dimensional packing problem arising in industry. The task is to pack a maximum number of rigid boxes with side length ratios of 4 : 2 : 1 into an irregularly shaped container. Motivated by the structure of manually constructed packings so far, we pursue a discrete approach. We discretize the shape of the container as well as the set of possible box placements....

1. Introduction One of the problems mentioned injl] (on p. 187) concerns the estimation of the magnitude of the largest number g(N) such that, from every sequence of N distinct natural numbers, one can always select a subsequence of g{N) integers with the property that no sum of two distinct integers of this subsequence belongs to the original sequence. It should be mentioned that the function ...

In this paper, we introduce the COmbinatorial Multi-Objective Multi-Armed Bandit (COMOMAB) problem that captures the challenges of combinatorial and multi-objective online learning simultaneously. In this setting, the goal of the learner is to choose an action at each time, whose reward vector is a linear combination of the reward vectors of the arms in the action, to learn the set of super Par...

Let w be a word in the free group of rank n ∈ N and let V(w) be the variety of groups defined by the law w = 1. Define V(w∗) to be the class of all groups G in which for any infinite subsets X1, . . . , Xn there exist xi ∈ Xi, 1 ≤ i ≤ n, such that w(x1, . . . , xn) = 1. Clearly, V(w) ∪ F ⊆ V(w ∗); F being the class of finite groups. In this paper, we investigate some words w and some certain cl...

We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the quotient of a finite solvable group modulo the second Fitting subgroup in terms of the number of irreducible character degrees of the group. Along the way, in...

Presented approach in polynomial time calculates large number of invariants for each vertex, which won’t change with graph isomorphism and should fully determine the graph. For example numbers of closed paths of length k for given starting vertex, what can be though as the diagonal terms of k-th power of the adjacency matrix. For k = 2 we would get degree of verities invariant, higher describes...

For many years I have enjoyed lecturing to groups of high school students about the excitement of mathematics. One diversion that never failed to capture their attention was as follows: Everyone was asked to write down a three digit number (abc with a > c), reverse it (to form cba), find the difference (as a three-digit number) between the two numbers, and add the difference to its own reverse....

This paper considers the parcel hub scheduling problem (PHSP) with unequal batch size inbound trailers, which is a combinatorial optimization problem commonly found in a parcel consolidation terminal in the parcel delivery industry (PDI). The problem consists of processing a large number of inbound trailers at a much smaller number of unload docks. The parcels in the inbound trailers must be un...