We show that the moments of the trace of a random unitary matrix have combinatorial interpretations in terms of longest increasing subsequences of permutations. To be precise, we s...
: We generalize the notion of pattern avoidance to arbitrary functions on ordered sets, and consider specifically three scenarios for permutations: linear, cyclic and hybrid, the f...
We study here the spectra of random lifts of graphs. Let G be a finite connected graph, and let the infinite tree T be its universal cover space. If λ1 and ρ are the spectral ...
Recently, David Chaum proposed an electronic voting scheme that combines visual cryptography and digital processing. It was designed to meet not only mathematical security standard...
Marcin Gomulkiewicz, Marek Klonowski, Miroslaw Kut...