Embedding Factorizations for 3-Uniform Hypergraphs II: $r$-Factorizations into $s$-Factorizations

Embedding Factorizations for 3-Uniform Hypergraphs

On the numbers of 1-factors and 1-factorizations of hypergraphs

A hypergraph G = (X,W ) is called d-uniform if each hyperedge w is a set of d vertices. A 1-factor of a hypergraph G is a set of hyperedges such that every vertex of the hypergraph is incident to exactly one hyperedge from the set. A 1factorization of G is a partition of all hyperedges of the hypergraph into disjoint 1-factors. The adjacency matrix of a d-uniform hypergraph G is the d-dimension...

A census of one-factorizations of the complete 3-uniform hypergraph of order 9

The one-factorizations of the complete 3-uniform hypergraph with 9 vertices, K 9 , are classified by means of an exhaustive computer search. It is shown that the number of isomorphism classes of such one-factorizations is 103 000.

Riordan group approaches in matrix factorizations

In this paper, we consider an arbitrary binary polynomial sequence {A_n} and then give a lower triangular matrix representation of this sequence. As main result, we obtain a factorization of the innite generalized Pascal matrix in terms of this new matrix, using a Riordan group approach. Further some interesting results and applications are derived.

Cycle factorizations and 1-faced graph embeddings

Consider factorizations into transpositions of an n-cycle in the symmetric group Sn. To every such factorization we assign a monomial in variables wij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we deduce a formula for the number of 1-fac...