English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The Ulam's metric is the minimal number of moves consisting in removal of oneelement from a permutation and its subsequent reinsertion in different place,to go between two given permutations. Thet elements that are not moved createlongest common subsequence of permutations. Aldous and Diaconis, in theirpaper, pointed that Ulam's metric had been introduced in the context ofquestions concerning sorting and tossing cards. In this paper we define andstudy Ulam's metric in highier dimensions: for dimension one the consideredobject is a pair of permutations, for dimension k it is a pair of k-tuples ofpermutations. Over encodings by k-tuples of permutations we define two duallyrelated hierarchies. Our very first motivation come from Murata at al. paper,in which pairs of permutations were used as representation of topologicalrelation between rectangles packed into minimal area with application to VLSIphysical design. Our results concern hardness, approximability, andparametrized complexity inside the hierarchies.

On Tractability of Ulams Metric in Highier Dimensions and Dually Related Hierarchies