Essays about: "Combinatorics"
Showing result 1 - 5 of 22 essays containing the word Combinatorics.
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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 kombinatorikAbstract : 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
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2. Improving software testing speed : using combinatorics
University essay from Linnéuniversitetet/Institutionen för datavetenskap och medieteknik (DM)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
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3. A Study on Poset Probability
University essay from Linköpings universitet/Algebra, geometri och diskret matematik; Linköpings universitet/Tekniska fakultetenAbstract : 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
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4. Cyclic Flats of Gammoids Via Dual Representation
University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikationAbstract : 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
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5. Counting Double-Descents and Double-Inversions in Permutations
University essay from Mälardalens högskola/Akademin för utbildning, kultur och kommunikationAbstract : 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