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/

Zendy Plus

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

Zendy Tools

Zendy Open

Conway and Lagarias observed that a triangular region T(m) in a hexagonallattice admits signed tiling by three-in-line polyominoes (tribones) if andonly if m=9d-1 or m=9d for some integer d. We apply the theory of Groebnerbases over integers to show that T(m) admits a signed tiling by n-in-linepolyominoes (n-bones) if and only if m=dn^2-1 or m=dn^2 for some integer d.Explicit description of the Groebner basis allows us to calculate the "Groebnerdiscrete volume" of a lattice region by applying the division algorithm to its`Newton polynomial'. Among immediate consequences is a description of the tilehomology group of the $n$-in-line polyomino.

Signed polyomino tilings by n-in-line polyominoes and Groebner bases