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A Note on Super Catalan Numbers
We show that the super Catalan numbers are special values of the Krawtchouk polynomials by deriving an expression for the super Catalan numbers in terms of a signed set.
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How many transactions per second can bitcoin really handle ? Theoretically
Transactions are arguably the most important part in the bitcoin mechanism, with everything else facilitating the proper creation, propagation and validation; culminating with their addition to theExpand
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Binomial options pricing has no closed-form solution
TLDR
We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach. Expand
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A combinatorial-probabilistic analysis of bitcoin attacks*
TLDR
We investigate the probability, and duration, of successful bitcoin attacks, and present a recurrence equation for the above-mentioned probability of success, that enables a very fast compilation of these probabilities. Expand
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Circular Digraph Walks, k-Balanced Strings, Lattice Paths and Chebychev Polynomials
TLDR
We count the number of walks of length $n$ on a circular digraph that cover all $k$ nodes in two ways. Expand
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A Note on Minimal Boolean Formula Size of One-Dimensional Cellular Automata
TLDR
We show that the maximal formula size for 3-input Boolean functions over basis Ω1 is 5. Expand
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