The average number of block interchanges needed to sort a permutation and a recent result of Stanley

The Average Number of Block Interchanges Needed to Sort a Permutation and a Recent Result Of

An Upper Bound on the Number of Circular Transpositions to Sort a Permutation

We consider the problem of upper bounding the number of circular transpositions needed to sort a permutation. It is well known that any permutation can be sorted using at most n(n−1) 2 adjacent transpositions. We show that, if we allow all adjacent transpositions, as well as the transposition that interchanges the element in position 1 with the element in the last position, then the number of t...

An improved algorithm for sorting by block-interchanges based on permutation groups

Given a chromosome represented by a permutation of genes, a block-interchanges is proposed as a generalized transposition that affects a chromosome by swapping two nonintersecting segments of genes. The problem of sorting by block-interchanges is to find a minimum series of block-interchanges for transforming one chromosome into another. In this paper, we present an O(n+ δ log n) time algorithm...

Investigating the Social, Economic and Environmental Impacts of Constructing Urban Interchanges (Comparison of the Main Interchanges in the city of Qazvin)

Traffic problems are the most prominent urban dilemmas, especially during recent years, since the capacity of old traffic arteries don’t meet the increasing volume of population and vehicles, therefore, adopting some measures in order to enhance the capacity of existing roads has been placed on the agenda of urban managers. Changing the existing intersections to over changes is one of these met...

On a special class of Stanley-Reisner ideals

For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...