Excessive[l,m]-factorizations

Holey factorizations

Holey factorizations of Kv1,v2,...,vn are a basic building block in the construction of Room frames. In this paper we give some necessary conditions for the existence of holey factorizations and give a complete enumeration for nonisomorphic sets of orthogonal holey factorizations of several special types.

Free Factorizations

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

Motivated by a 40-year-old problem due to Peter Cameron on extending partial parallelisms, we provide necessary and sufficient conditions under which one can extend an r-factorization of a complete 3-uniform hypergraph on m vertices, K3 m, to an s-factorization of K3 n. This generalizes an existing result of Baranyai and Brouwer–where they proved it for the case r = s = 1.

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.

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, 23 (2), 51 (1970)), and related representations termed q1q2 representations (together with their conjugates) are analysed, as well a...