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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Dissections of polytopes are a well-studied subject by geometers as well asrecreational mathematicians. A recent application in coding theory arises fromthe problem of parameterizing binary vectors of constant Hamming weight whichhas been shown previously to be equivalent to the problem of dissecting atetrahedron to a brick. Applications of dissections also arise in problemsrelated to the construction of analog codes.  Here we consider the rectangle-to-rectangle dissection due to Montucla.Montucla's dissection is first reinterpreted in terms of the Two Tile Theorem.Based on this, a cube-to-brick dissection is developed in $\mathbb{R}^n$. Wepresent a linear time algorithm (in $n$) that computes the dissection, i.e.determines a point in the cube given a point in a specific realization of thebrick. An application of this algorithm to a previously reported analog codingscheme is also discussed.

A Generalization of Montucla's Rectangle-to-Rectangle Dissection to Higher Dimensions