HUN-REN Institute for Computer Science and Control

A complete dichotomy theorem on the sparse t-uniform hypergraphicality problem

We prove a complete dichotomy theorem for the parameterized sparse t -uniform hypergraphical degree sequence problem, sparse - t - uni - HDS α ′ , α . For any fixed t ≥ 3 , given parameters 0 ≤ α ′ ≤ α < t − 1 , the input consists of degree sequences D of length n with degrees be...

Swiss-system chess tournaments and unfairness

Abstract The Swiss system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess tournaments if an odd number of...

Intrinsic volumes of the quantum state space and mutually unbiased bases

Abstract Previous studies on the geometrical properties of the state space of a finite-level quantum system have determined its volume and surface area. Building on this foundation, we derive explicit formulas for two additional intrinsic volume quantities. The question of whethe...