Some approaches for solving the general (t,k)-design existence problem and other related problems

Authors:
Amitava Bhattacharya;Navin M. Singhi
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

In this short survey, some approaches that can be used to solve the generalized (t,k)-design problem are considered. Special cases of the generalized (t,k)-design problem include well-known conjectures for t-designs, degree sequences of graphs and hypergraphs, and partial Steiner systems. Also described are some related problems such as the characterization of 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.