Reconstruction of permutations from their erroneous patterns

Reconstruction of permutations distorted by single transposition errors

The reconstruction problem for permutations on n elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any n ≥ 3 an unknown permutation is uniquely reconstructible from 4 distinct permutations at transposition distance at most one from the unknown permutation. The transposition distance between two permutations is defined a...

On reconstruction of signed permutations distorted by reversal errors

The problem of reconstructing signed permutations on n elements from their erroneous patterns distorted by reversal errors is considered in this paper.A reversal is the operation of taking a segment of the signed permutation, reversing it, and flipping the signs of its elements. The reversal metric is defined as the least number of reversals transforming one signed permutation into another. It ...

EFL Teachers’ Reconstruction of Student-Writers’ Intentions in Erroneous Sentences: The Role of Context

Note on Packing Patterns in Colored Permutations

Packing patterns in permutations concerns finding the permutation with the maximum number of a prescribed pattern. In 2002, Albert, Atkinson, Handley, Holton and Stromquist showed that there always exists a layered permutation containing the maximum number of a layered pattern among all permutations of length n. Consequently the packing density for all but two (up to equivalence) patterns up to...

Equivalence Classes of Permutations Modulo Replacements Between 123 and Two-Integer Patterns

We explore a new type of replacement of patterns in permutations, suggested by James Propp, that does not preserve the length of permutations. In particular, we focus on replacements between 123 and a pattern of two integer elements. We apply these replacements in the classical sense; that is, the elements being replaced need not be adjacent in position or value. Given each replacement, the set...