Essays about: "combinatorics"

Showing result 1 - 5 of 22 essays containing the word combinatorics.

  1. 1. Applications of Random Walks : How Random Walks Are Used in Wilson's Algorithm and How They Connect to Electrical Networks

    University essay from Uppsala universitet/Sannolikhetsteori och kombinatorik

    Author : Erik Jonsson; [2024]
    Keywords : Random Walks; Wilson s Algorithm; Electrical Networks; Pòlya s theorem;

    Abstract : In this master thesis we will show how random walks are used in Wilson's algorithm to generate spanning trees of graphs, and how they can be used to calculate the number of spanning trees in a graph. We will also explore the connection between electrical networks and random walks, and how this connection can be exploited to prove Pólya's theorem (normally proved with probability and combinatorics) using electrical arguments. READ MORE

  3. 2. Improving software testing speed : using combinatorics

    University essay from Linnéuniversitetet/Institutionen för datavetenskap och medieteknik (DM)

    Author : Sami Mwanje; [2023]
    Keywords : Testing optimization; Test time reduction; Test quality; Machine learning; Mathematical models; Software testing; Combinatorial testing; Au- tomation; Embedded systems; Pairwise Testing;

    Abstract : Embedded systems hold immense potential, but their integration into advanced devices comes with significant costs. Malfunctions in these systems can result inequipment failures, posing serious risks and potential accidents. READ MORE

  4. 3. A Study on Poset Probability

    University essay from Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakulteten

    Author : Albin Jaldevik; [2022]
    Keywords : Discrete mathematics; Order theory; Combinatorics; Partially ordered set; Poset; Linear extension; Topological sorting; Probability; Partition; Young diagram;

    Abstract : Let be a finite poset (partially ordered set) with cardinality . A linear extension of is an order-preserving bijection : , that is, if in then . We define the poset probability as the proportion of linear extensions where . We are primarily interested in for incomparable elements . READ MORE

  5. 4. Cyclic Flats of Gammoids Via Dual Representation

    University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

    Author : Emil Gustafsson; [2022]
    Keywords : Matroids; Gammoids; Cyclic flats; dual matroids;

    Abstract : Matorids provide useful abstraction in combinatorics and have a number of applications in many areas. Gammoids,  which is one of many classes of matroids, and they can be represented by directed graphs, which make them easy to visualize. READ MORE

  6. 5. Counting Double-Descents and Double-Inversions in Permutations

    University essay from Mälardalens högskola/Akademin för utbildning, kultur och kommunikation

    Author : Jonas Boberg; [2021]
    Keywords : Combinatorics; Permutations; Permutation Statistics; Descent; Inversion;

    Abstract : In this paper, new variations of some well-known permutation statistics are introduced and studied. Firstly, a double-descent of a permutation π is defined as a position i where πi ≥ 2πi+1. By proofs by induction and direct proofs, recursive and explicit expressions for the number of n-permutations with k double-descents are presented. READ MORE