Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...

Unlike the method without pivoting, Gaussian elimination with partial pivoting consecutively applies row permutation to matrix A in order to avoid possible akk diagonal entries of matrix A being equal to zero. Gaussian elimination with partial pivoting solves the matrix equation Ax = b decomposing matrix A into a lower L and upper U triangular matrices such that PA = LU, where P is a row permut...

Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce notion permutation resemblance a function, which looks to measure distance given map is from being permutation. We prove several results concerning permutation resemblance and show how it can ...

Linkage analysis in multivariate or longitudinal context presents both statistical and computational challenges. The permutation test can be used to avoid some of the statistical challenges, but it substantially adds to the computational burden. Utilizing the distributional dependencies between p (defined as the proportion of alleles at a locus that are identical by descent (IBD) for a pairs of...

MOTIVATION In analyses of microarray data with a design of different biological conditions, ranking genes by their differential 'importance' is often desired so that biologists can focus research on a small subset of genes that are most likely related to the experiment conditions. Permutation methods are often recommended and used, in place of their parametric counterparts, due to the small sam...