Talk:WikiJournal of Science/Affine symmetric group

Plagiarism check
✅ Report from WMF copyvios tool: only similarities are common phrases or reference names (e.g. "The generalized Robinson–Schensted algorithm on the affine Weyl group of type"). T.Shafee(Evo&#65120;Evo)talk 04:53, 12 June 2020 (UTC)

Editorial notes

 * Thank you - the changes are great. It would be ideal, if possible, to have a short non-technical summary in addition to the abstract aimed at someone even less expert in the area. The aim is to have someone with as little expertise as possible, be able to understand some core feature of the topic (sometimes requiring synonyms for technical terms, analogies, and cautious simplification). There's no strict style for acknowledgements currently (short guidance here), though we may eventually more to include more structured data in future (STARDIT). T.Shafee(Evo&#65120;Evo)talk 03:27, 30 March 2021 (UTC)
 * Thank you for your responses. I have added an acknowledgements section to the paper.  Here is an attempt at a lay summary.
 * "The affine symmetric group is a mathematical structure that describes the symmetries of the number line and the regular triangular tiling of the plane, as well as related higher dimensional objects. The individual elements of the affine symmetric group, which are called affine permutations, may also be interpreted as certain periodic rearrangements of the set of integers (..., −2, −1, 0, 1, 2, ...), as well as in purely algebraic terms. Unlike the symmetries of a single polygon or polyhedron and the collection of rearrangements of a finite set, there are infinitely many affine permutations.  For this reason, the affine symmetric group provides an avenue to extend the study of symmetries of polyhedra or of groups of permutations to the infinite case.  As a result, the affine symmetric group is of interest in several areas of mathematics, including combinatorics and representation theory.  It also has connections with mathematical objects that were originally studied for independent reasons, such as complex reflection groups and juggling sequences."
 * Joel Brewster Lewis (discuss • contribs) 21:18, 19 April 2021 (UTC)
 * Excellent, thank you. These summaries are notoriously hard to write! I've made a suggested version below, but please check if any is over-simplified to the point of incorrectness:
 * "Flat, straight-edged shapes (like trianges) or 3D ones (like pyramids) have only a finite number of symmetries. In contrast, the affine symmetric group is a way to mathematically describe all the symmetries possible of triangular tiles arranged on a infinitely large flat surface. As with many subjects in mathematics, it can also be thought of in a number ways: for example it also describes the symetries of the infinitely long number line, or the posible repeating arrangements of all integers (..., −2, −1, 0, 1, 2, ...). As a result, studying the affine symmetric group extends the study of symmetries of polyhedra or of groups of permutations to the infinite case. It also connects several topics in mathematics that were originally studied for independent reasons (such as combinatorics and representation theory) ranging from complex reflection groups to juggling sequences."
 * T.Shafee(Evo&#65120;Evo)talk 11:48, 20 April 2021 (UTC)
 * Thanks for your edits! It is very hard to remember how much of technical language is jargon.  I have tweaked your latest version slightly, and I think we are converging on something quite reasonable:
 * "Flat, straight-edged shapes (like triangles) or 3D ones (like pyramids) have only a finite number of symmetries. In contrast, the affine symmetric group is a way to mathematically describe all the symmetries possible when an infinitely large flat surface is covered by triangular tiles. As with many subjects in mathematics, it can also be thought of in a number ways: for example, it also describes the symmetries of the infinitely long number line, or the possible arrangements of all integers (..., −2, −1, 0, 1, 2, ...) with certain repetitive patterns. As a result, studying the affine symmetric group extends the study of symmetries of polyhedra or of groups of permutations to the infinite case. It also connects several topics in mathematics that were originally studied for independent reasons, ranging from complex reflection groups to juggling sequences."
 * Joel Brewster Lewis (discuss • contribs) 15:02, 20 April 2021 (UTC)
 * Joel Brewster Lewis (discuss • contribs) 15:02, 20 April 2021 (UTC)