Tensors are becoming increasingly common in data mining, and consequently, tensor factorizations are becoming more and more important tools for data miners. When the data is binary, it is natural to ask if we can factorize it into binary factors while simultaneously making sure that the reconstructed tensor is still binary. Such factorizations, called Boolean tensor factorizations, can provide ...

We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 . . . n) into a product of smaller cycles of given length and trees of a certain structure. A factorization has the type α = (α2, α3, · · · ) if it has αj factors of length j. Inequivalent factorizations are defined up to reordering of commuting factors. A factorization is minimal if no factorizations of a ...

Numerically reliable state space algorithms are proposed for computing the following stable coprime factorizations of rational matrices: 1) factorizations with least order denominators; 2) factorizations with inner denominators; and 3) factorizations with proper stable factors. The new algorithms are based on a recursive generalized Schur algorithm for pole assignment. They are generally applic...

Numerically reliable state space algorithms are proposed for computing the following stable coprime factorizations of rational matrices factorizations with least order denominators factorizations with inner denominators and factorizations with proper stable factors The new algorithms are based on a recursive generalized Schur algorithm for pole assignment They are generally applicable regardles...

Ziv-Lempel and Crochemore factorization are two kinds of factorizations of words related to text processing. In this paper, we find these factorizations for standard epiesturmian words. Thus the previously known c-factorization of standard Sturmian words is provided as a special case. Moreover, the two factorizations are compared.

Factorizations of various functions are discussed. Complete factorizations of certain classes of functions are given. In particular it is shown that there exist primes of arbitrary growth.

Following what is basically Kummer’s relatively neglected approach to non-unique factorization, we determine the structure of the irreducible factorizations of an element n in the ring of integers of a number field K. Consequently, we give a combinatorial expression for the number of irreducible factorizations of n in the ring. When K is quadratic, we show in certain cases how quadratic forms c...

Motivation Many methods for transcript-level abundance estimation reduce the computational burden associated with the iterative algorithms they use by adopting an approximate factorization of the likelihood function they optimize. This leads to considerably faster convergence of the optimization procedure, since each round of e.g. the EM algorithm, can execute much more quickly. However, these ...

An equivalent relation between transitive 1-factorizations of arctransitive graphs and factorizations of their automorphism groups is established. This relation provides a method for constructing and characterizing transitive 1-factorizations for certain classes of arc-transitive graphs. Then a characterization is given of 2-arc-transitive graphs which have transitive 1factorizations. In this c...

In this paper, we revisit the lexical and modular factorization of the middle level graph. We present new and simple definitions of such factorizations, and thus reveal their inner structures. Based on our new results, we present optimum algorithms for computing these 1-factorizations. In addition, we provide interesting applications of these factorizations in game theory. 1998 ACM Subject Clas...