Combinatorial problems arising from permutations and hypergraphs

The present work fits into the field of Combinatorics. The object of study are classes of discrete objects that can be characterized by means of combinatorial properties. More precisely, the treated structures are subfamilies of known combinatorial classes such as pattern-avoiding permutations, lattice paths, graphs and hypergraphs. The problems addressed in this PhD thesis use different approaches for their resolution. For example, some results have been obtained by developing algorithms on graphs and hypergraphs, using succession rules, establishing bijections with other known combinatorial structures. The results can be divided into two research areas: 1. Problems arising from Enumerative Combinatorics: (a) Pattern-avoiding permutations (b) Doubly Symmetric Words 2. Problems arising from Graphs and Hypergraphs (a) Max k-cut game: a problem arising from graphs in Game Theory (b) Application of graphs to Reaction Systems (c) Reconstruction of Hypergraphs from partial informations and Null Hypergraphs