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Results tagged with co.combinatorics
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user 32389
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
19
votes
Accepted
Ordinary Generating Function for Bell Numbers
The proof is given, for example, in http://www.sciencedirect.com/science/article/pii/S0097316503000141 (Bell numbers, their relatives, and algebraic differential equations, by Martin Klazar). Namely i …
- 16.5k
10
votes
volume over a hypercube, over simplex: twist by Euler numbers
This is only a partial answer. The Beukers-Kolk-Calabi change of variables
$$x_1=\frac{\sin{u_1}}{\cos{u_2}},\;\;x_2=\frac{\sin{u_2}}{\cos{u_3}},\ldots,
\;x_{n-1}=\frac{\sin{u_{n-1}}}{\cos{u_n}},\;\;x …
- 16.5k
8
votes
What is the amplituhedron?
In addition to Carlo Beenakker's wonderful answer: it seems Penrose's twistor formalism (twistor diagrams) plays a central role in this amplituhedron business.
See http://www.twistordiagrams.org.uk/pa …
- 16.5k
7
votes
Reference on Persistent Homology
Maybe the following papers will be useful:
https://www.cambridge.org/core/journals/acta-numerica/article/topological-pattern-recognition-for-point-cloud-data/BB0DA0F0EBD79809C563AF80B555A23C (Topolo …
- 16.5k
5
votes
Combinatorial interpretation of composition of power series?
It seems solutions of the functional equation $g(g(t))=t$ are related to pseudo-involutions of the Riordan group. See http://www.sciencedirect.com/science/article/pii/S0166218X0900016X (Riordan group …
- 16.5k
4
votes
Why do Bernoulli numbers arise everywhere?
Apart from pure mathematics, the Bernoulli numbers appear quite often in quantum field theory computations due to their relation with the Riemann zeta function.
The fundamental reason for this is expla …
4
votes
Accepted
Young tableaux for exceptional Lie algebras
Young diagrams for the exceptional Lie algebras are considered in the book https://press.princeton.edu/titles/8839.html (Group Theory: Birdtracks, Lie's, and Exceptional Groups, by Predrag Cvitanovic) …
- 16.5k
3
votes
Who constructed the projective plane of order $4$ from $K_6$?
Maybe this book http://www.google.com/search?tbo=p&tbm=bks&q=isbn:3540617868 (Peter Dembowski, Finite Geometries) can help. It has extensive bibliography. Was reprinted in 1997: http://www.amazon.com/ …
- 16.5k
3
votes
Accepted
Reference for Frobenius’s proof of Schur’s finite version of the Rogers - Ramanujan identities
Early history of the Rogers-Ramanujan identities is discussed by Hardy in "Ramanujan: Twelve lectures suggested by his life and work", Chelsea,
third edition, 1978. But Hardy doesn't mention Frobenius …
- 16.5k
2
votes
Accepted
English translation of Witt's paper on the Mathieu groups?
In light of this book http://www.amazon.co.uk/Collected-Papers-Abhandlungen-Ernst-Witt/dp/3642150950 (Collected Papers - Gesammelte Abhandlungen by Ernst Witt) it seems very few (if any) of Witt's pap …
- 16.5k
2
votes
Can we make 101 almost perfect banknotes from 100?
This video http://thekidshouldseethis.com/post/62804856022 shows a possible solution (well, not for banknotes but for chocolate and one piece is only about 4% in size). This is a variant of Paul Curry …
- 16.5k
1
vote
2-adic Logarithm and Resistance of n-dimensional Cube
The following article https://arxiv.org/abs/0904.1757 (The Hypercube of Resistors, Asymptotic Expansions, and Preferential Arrangements, by Nicholas Pippenger. Published in Mathematics Magazine 83(N5) …
- 16.5k