Unscrambling the hidden secrets of superpermutations

/? Knuth's 4A volume of The Art of Computer Programming site:github.com : https://www.google.com/search?q=Knuth%27s+4A+volume+of+The+A... :

> Generate {n-tuples, permutations, combinations, partitions, set partitions, trees,} with combinatorial patterns

Combinatorics: https://en.wikipedia.org/wiki/Combinatorics

- Exercise: Permutations [& Combinations]: https://rosettacode.org/wiki/Permutations#Python https://rosettacode.org/wiki/Combinations_and_permutations#P...

- Exercise: Rewrite itertools.product as a generator that yields in a different order than itertools.product; write a different graph traversal that also covers without repetition

- Exercise: The Birthday problem and actual probability of cryptographic hash collision given hash length n: https://en.wikipedia.org/wiki/Birthday_problem

- Exercise: The Gambler's Fallacy: Given a sequence of random values that satisfy many of the tests in e.g. Google/paranoid_crypto.lib.randomness_tests, where would Gambler's Fallacy have caused loss? https://en.wikipedia.org/wiki/Gambler%27s_fallacy https://github.com/google/paranoid_crypto/tree/main/paranoid...

Combinatorics and physics: https://en.wikipedia.org/wiki/Combinatorics_and_physics

/?hnlog Ctrl-f Hilbert :

"Matrices and Graph" https://news.ycombinator.com/item?id=36739579 :

> [ Multigraph, networkx.MultiDiGraph , RDF Linked Data ]

> Tensor product of graphs: https://en.wikipedia.org/wiki/Tensor_product_of_graphs

> Hilbert space: https://en.wikipedia.org/wiki/Hilbert_space :

>> In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space.

>> [...] The inner product between two state vectors is a complex number known as a probability amplitude.

Wave interference > Quantum interference: https://en.wikipedia.org/wiki/Wave_interference#Quantum_inte...

EM waves have amplitude in the interval [-1,1] or [-inf, +inf].

With EM waves we typically model constructive interference and destructive interference.

There is also a particle-like phononic quantum wave interpretation of EM waves.

Quantum waves are in the interval [0,1].

Quantum embedding is the process and study of encoding data as wave functions with e.g. phase.

https://news.ycombinator.com/item?id=38255569 :

> How many ways are there to roll a {2, 8, or 6}-sided die with qubits and quantum embedding?

Quantum superposition and combinatorics; why can't the quantum simulator run this code like an actual QC?

"Where does energy go during destructive interference?" (2018) https://news.ycombinator.com/item?id=32421509 :

> From Conservation_of_energy#Quantum_theory https://en.wikipedia.org/wiki/Conservation_of_energy#Quantum... :

>> In quantum mechanics, energy of a quantum system is described by a self-adjoint (or Hermitian) operator called the Hamiltonian, which acts on the Hilbert space (or a space of wave functions) of the system. If the Hamiltonian is a time-independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent [If the Hamiltonian is a time-independent operator]

{Employee, Conference, Computational resource} Scheduling with priority: https://news.ycombinator.com/item?id=22589911 :

> https://en.wikipedia.org/wiki/Hilbert_curve_scheduling :

>> [...] the Hilbert curve scheduling method turns a multidimensional task allocation problem into a one-dimensional space filling problem using Hilbert curves, assigning related tasks to locations with higher levels of proximity.[1] Other space filling curves may also be used in various computing applications for similar purposes. [2]

And then fluids.

Computational Fluid Dynamics is still one of the harder problems in classical high performance computing and quantum computing because it is a combinatorically hard problem to model every possible fluid outcome in order to predict the most likely outcome(s).

/?hnlog Navier [e Euler, Stokes,] :

- "Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations" https://news.ycombinator.com/item?id=31049608 :

> [awesome-fluid dynamics, jax-cfd,]

And then Evolutionary Algorithms,

- Infinite Monkey Theorem: https://en.wikipedia.org/wiki/Infinite_monkey_theorem

- https://news.ycombinator.com/item?id=39110110#39139198 :

> Holman's "elegant normal form",

Evolutionary Algorithms > Convergence: https://en.wikipedia.org/wiki/Evolutionary_algorithm#Converg... :

> For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of convergence under the condition that an optimum exists. Without loss of generality, a maximum search is assumed for the proof: [...]

It's frustrating the article just ends right there. "Then in 2014 someone did even better. The End." What was the new technique?

I’m not a combinatorist, but I’m also appalled that two separate Quanta articles didn’t mention De Bruijn sequences.

I see they are trying to spice up math articles, but this is ridiculous !