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.

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 the… Expand

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

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