Petra Cini, composer and pianist, gave a special #nikhef theory seminar on musical representations: violence, purity and mathematics
#grouptheory
0 posts0 participants0 posts today
Drafted a 3rd inquiry activity for D3 and D4 play with flips and rotations.
I am hoping it's not to dry. I'll read through it again tomorrow.
I've kind of always wondered what the point of definitions like a group is a non-empty set \(G\) with a binary operation \(d\) satisfying \(d(d(d(z,d(x, d(x,x))),d(z,d(y,d(x,x)))),x) = y\) is, other than because we can, but https://math.stackexchange.com/a/4366021 offers one such answer in terms of homotopy type
Mathematics Stack ExchangeLooking for 1952 paper of Higman and NeumannI am looking for the paper
Graham Higman and Bernhard Hermann Neumann,
Groups as groupoids with one law,
Publicationes Mathematicae Debrecen 2 (1952), 215–221.
In it, the authors prove (among other
searching for any structures / theory that involve a particular operation on non-empty lists of postitive integers like "the length of the list multiplied by the least common multiple of all the items in the list"
any ideas? references to any literature would be very appreciated if you know of any.
Share via
existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way.
einstein problem can be seen as a natural extension of the second part of Hilbert's eighteenth problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral.[3] Such anisohedral tiles were found by Karl Reinhardt in 1928, but these anisohedral tiles all tile space periodically.
Partition of a plane in closed set - tile
2022, hobbyist David Smith discovered a "hat"-shaped tile formed from eight copies of a 60°–90°–120°–90° kite (deltoidal trihexagonals), glued edge-to-edge, which seemed to only tile the plane aperiodically.[8] Smith recruited help from mathematicians Craig S. Kaplan, Joseph Samuel Myers, and Chaim Goodman-Strauss, and in March 2023 the group posted a preprint proving that the hat, when considered with its mirror image, forms an aperiodic prototile set.[
Wiki
#grouptheory
New 
Release! Introduction to Group Theory: An Activity-Based Approach by Joe Fox #books #ebooks #math #grouptheory
This book is an introduction to group theory suitable for an introductory course in abstract algebra. Much of the content is delegated to a series of activities that are meant to be worked through by the students with the help of the instructor.
Find it on Leanpub!
Riffs and Rotes • Happy New Year 2025
• https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/
\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)
\( \text{Then} ~ 2025
= 81 \cdot 25
= 3^4 5^2 \)
\( = {p_2}^4 {p_3}^2
= {p_2}^{{p_1}^{p_1}} {p_3}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1}
= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)
No information is lost by dropping the terminal 1s. Thus we may write the following form.
\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]
The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.
Riff 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png
Rote 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png
Reference —
Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes
#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes
Want to formalize something in Mizar but don't know where to begin?
I'm starting a new series of posts with project ideas, starting with Loops! They're needed to formalize the sporadic groups (as found in, e.g., Aschbacher's book "Sporadic Groups").
Ariadne's Thread · Loops in MizarProject Summary: Formalize Section 12 of Aschbacher’s Sporadic Groups. This is actually a surprisingly straightforward and standalone formalization project in Mizar: formalize Moufang loops i…
A shop called "Wreath Products" that sells mathematical puzzle toys, mobiles (like for baby cribs or art)...and, sure, also decorative wreaths.
Sat Dec 7, 2024 on zoom & in-person
Session in memory of Richard Parker at the annual Nikolaus conference at Aachen (on group & representation theory). Main speakers:
Gerhard Hiß
Gabriele Nebe
Colva Roney-Dougal
www.math.rwth-aachen.deNikolaus Conference 2024
This textbook has heavy “demon summoning” vibes to it 
[New Blog Post] Coset Enumeration using Equality Saturation https://www.philipzucker.com/coset_enum_egraph/ #egraph #grouptheory #algebra
Hey There Buddo! · Coset Enumeration using Equality SaturationAs I was digging into computational group theory for string Knuth Bendix completion goodness I noted that coset enumeration aka Todd-Coxeter, one of the mainstay algorithms of computational group theory, mechanically looks quite a bit like equality saturation. This is interesting in its own right but also as a source of controlled benchmarks for equality saturation systems.
A normal subpost is a subpost whose left and right coposts are equal.
#GroupTheory #SubPost
Can any experts comment on the quality of this 97-year-old's research?
arXiv.orgInvariants cohomologiques mod 2 et invariants de Witt des groupes alternésWe determine the cohomological invariants and the Witt invariants of the alternating group $A_n$.
Formalizing groups in Mizar, a review and assessment. (Originally, I wanted to entitle this "Get in losers, we're formalizing groups", but my accordion player vetoed it.)
This is an experiment where we start with "book definitions" as found in, say, Bourbaki, and then work our way towards its corresponding formalization in #Mizar.
https://thmprover.wordpress.com/2024/02/08/how-mizar-formalizes-groups/
Ariadne's Thread · How Mizar Formalizes GroupsWhenever I learn a new proof assistant, I always look at how groups are formalized because they’re a suitably simple gadget which can easily be formalized, but it’s mathematically deep …
Looking forward to tomorrow’s 2nd workshop on #symmetry, invariance and #NeuralRepresentations at the #BernsteinConference: #GroupTheory, #manifolds, and #Euclidean vs #nonEuclidean #geometry #perception … I’m pretty excited 
#CompNeuro #computationalneuroscience
