Discovered this mildly interesting identity ( in 2019 I think ) using double counting technique while trying to solve a five thirty eight riddler. Probably follows directly from some property of the Bernoulli numbers.
The left and right hand sides are equal to the number of non-increasing sequences of fixed length generated from a set of ordered alphabet - 9873, 6661, 8866 for example are valid sequences of length 4 out of a total of 4 + 9 -1 C 4 such sequences generated using 1,2, ... 9.
The right hand side can be trivially arrived at by seeing how this is equivalent to the familiar distributing-n-objects-into-k-slots thingy and the left hand side is derived using recurrence relations detailed in the link below.
https://t.co/gJO6obOl0C
Code
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https://t.co/TyIn9lshAq
#combinatorics #fivethirtyeight #riddler #doublecounting
I was jamming with Claude on Grassmann's Punktrechnung framework and got fascinated by how vectors arise here as a special case of centroidal addition of weighted points and thought to myself I should ask what exotic entity will then emerge from point wedging and lo and behold it’s a fucking bound vector!
The image is not merely a texture to be deformed. It is a topological manifold whose medial structure encodes its own articulation, and whose distance field reveals its own mass.
My dear front-end developers (and anyone who’s interested in the future of interfaces):
I have crawled through depths of hell to bring you, for the foreseeable years, one of the more important foundational pieces of UI engineering (if not in implementation then certainly at least in concept):
Fast, accurate and comprehensive userland text measurement algorithm in pure TypeScript, usable for laying out entire web pages without CSS, bypassing DOM measurements and reflow
Implemented a sliding window based mean n-gram histogram vector solution for fingerprinting embedding models after coming across a transformer based solution by Han Xiao of Jina AI and it surprisingly works better than I expected. Link to Colab notebook below.
https://t.co/xVQOhHAXCc
Formal grammar generates a string where alphabets correspond to Image mutation algorithms - some of them original. They act on input image successively. Very rich space it appears to be. Inspired by a similar project by @allnoteson