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Discrete Mathematics and Combinatorics Commons™
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Full-Text Articles in Discrete Mathematics and Combinatorics
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Ronald Greenberg
Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.
Cycle Lengths Of Θ-Biased Random Permutations, Tongjia Shi
Cycle Lengths Of Θ-Biased Random Permutations, Tongjia Shi
HMC Senior Theses
Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θK, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The mth moment of the rth longest cycle of a random permutation is Θ(nm), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or …