Enumerative #Combinatorics principle:
Whenever you have an integer sequence (a_n) for which every a_n has only small prime factors, there is a product counting formula behind it.
Meta reason:
Numbers do not only have small prime factors by coincidence. There is a reason behind it.
#MathSky #Math
In combinatorics, this is a *linear extension*. And the analogue of the existence statement is
"A directed graph defines a poset if and only if the graph is acyclic".
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Geometric local systems on very general curves and isomonodromy, JAMS
Canonical representations of surface groups, Annals
I've recently been talking a bit about how difficult it is to carefully check even well-written mathematics. I want to try to explain something about this by telling the story of some errors in the literature that (in part) led to the two papers below. 1/n
Please help, my cookies are approximating a Voronoi tessellation.
In one year, the Institute for Computational and Experimental Research in Mathematics (ICERM) will have the following exciting program:
Categorification and Computation in Algebraic Combinatorics
Sep 3 - Dec 5, 2025
icerm.brown.edu/program/seme...
#Mathematics #Combinatorics #MathSky
D&D Combinatorics xkcd.com/3015
* Electronic Journal of Combinatorics (www.combinatorics.org)
* Algebraic Combinatorics (alco.centre-mersenne.org)
Feel free to add more in the comments!
#Mathematics #Combinatorics #OpenAccess #MathSky #MathJournals #Research
2/2
Do you want to publish your Combinatorics research in diamond open access journals, with no fees for authors or readers ?
Here are some first great options to consider:
* Combinatorial Theory, which has a double-anonymous review process (combinatorial-theory.org)
1/2
Sure you can. I'd give it a try.
Combinatorics is a research field for the future!
"We've got this feeling that there's a whole extraordinary talented generation coming up"
Dear Combinatorialists around the world
This account is still empty, but we hope the combinatorics community to grow!
You are all invited to take over this account for a week or two to share your views on combinatorics.
#Combinatorics #Mathematics #MathSky