Some approaches for solving the general (t,k) ( t , k ) -design existence problem and other related problems
In this short survey, some approaches that can be used to solve the generalized (t,k) ( t , k ) -design problem are considered. Special cases of the generalized (t,k) ( t , k ) -design problem include well-known conjectures for t t -designs, degree sequences of graphs and hypergraphs, and partial Steiner systems. Also described are some related problems such as the characterization of f f -vectors of pure simplicial complexes, which are well known but little understood. Some suggestions how enumerative and polyhedral techniques may help are also described.
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