Motivated by applications to string processing, we introduce variants of the Lyndon factorization called inverse Lyndon factorizations. Their factors, named inverse Lyndon words, are in a class that strictly contains anti-Lyndon words, that is Lyndon words with respect to the inverse lexicographic order. We prove that any nonempty word w admits a canonical inverse Lyndon factorization, named IC...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...

An independent (algebraic) proof is given of the factorization property Grand Jacobian corresponding to anticanonical transformations in BV formalism.

Row-merge trees for forming the QR factorization of a sparse matrix A are closely related to elimination trees for the Cholesky factorization of ATA. Row-merge trees predict the exact fill-in (assuming no numerical cancellation) provided A satisfies the strong Hall property, but over-estimates the fill-in in general. However, here a fast and simple post-processing step for rowmerge trees is pre...

Row-merge trees for forming the QR factorization of a sparse matrix A are closely related to elimination trees for the Cholesky factorization of ATA. Row-merge trees predict the exact fill-in (assuming no numerical cancellation) provided A satisfies the strong Hall property, but over-estimates the fill-in in general. However, here a fast and simple post-processing step for rowmerge trees is pre...

The corona factorization property is a property with connections to extension theory, K-theory and the structure of C *-algebras. This paper is a short survey of the subject, together with some new results and open questions.

The corona factorization property is a property with connections to extension theory, K-theory and the structure of C *-algebras. This paper is a short survey of the subject, together with some new results and open questions.