The existence of designs II

Abstract

We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with extra edge data, such as colours and orders, and so incorporates a wide range of variations on the basic design problem, notably Baranyai-type generalisations, such as resolvable hypergraph designs, large sets of hypergraph designs and decompositions of designs by designs. Our method also gives approximate counting results, which is new for many structures whose existence was previously known, such as high dimensional permutations or Sudoku squares.

64 pages

References in corpus (1)

• New bounds on the number of n-queens configurations

Cited by in corpus (7)

• Tight paths in convex geometric hypergraphs
• Constructions of Pairs of Orthogonal Latin Cubes
• Ringel's tree packing conjecture in quasirandom graphs
• Euler tours in hypergraphs
• On partial Steiner $(n,r,\ell )$-system process
• Note on random Latin squares and the triangle removal process
• A note on hypergraphs without non-trivial intersecting subgraphs