RE: https://mathstodon.xyz/@kangmeister/116136852073418222
It was almost exactly two years ago in Lunteren after a pitch by Ton de Kok (director of CWI at the time) that the idea for this popped into mind. And now (after a lot of hard work!) it is in full swing. An exciting mix of people at the confluence of combinatorics, algorithms, probability, brought together in Amsterdam over the next couple of months!
A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.
However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/
https://arxiv.org/abs/2603.12358
Here is the *third* manuscript coming out of the "Topics in Ramsey theory" online-only problem-solving session (https://sparse-graphs.mimuw.edu.pl/doku.php?id=sessions:2025sessions:2025session1) of the Sparse (Graphs) Coalition, which took place less than a year ago.
It is still surprising to realise what one can make of such events, if they are set up well.
#combinatorics #remoteconferences #graphtheory #extremalcombinatorics #openscience
An ordered graph is a graph whose vertex set is equipped with a total order. The ordered complete graph $K_N^<$ is the complete graph with vertex set $[N]$ equipped with the natural ordering of the integers. Given an ordered graph $H$, the ordered Ramsey number $R_<(H)$ is the smallest integer $N$ such that every red/blue edge-colouring of $K_N^<$ contains a monochromatic copy of $H$ with vertices appearing in the same relative order as in $H$. Balko, Cibulka, Král, and Kyn\v cl asked whether, among all ordered paths on $n$ vertices, the ordered Ramsey number is minimised by the alternating path $\mathrm{AP}_n$ -- the ordered path with vertex set $[n]$ such that the vertices encountered along the path are $1, n, 2, n - 1,3, n-2,\dots$. Motivated by this problem, we make progress on establishing the value of $R_<(\mathrm{AP}_n)$ by proving that \[ R_{<}(\mathrm{AP}_n)\leq \left(2+\frac{\sqrt{2}}{2}+o(1)\right)n. \] We then use similar methods to determine the exact ordered Turán number of $\mathrm{AP}_n$, and study the ordered Ramsey and Turán numbers of several related ordered paths.
No wonder #combinatorics is hard!
#mathematics #maths #math
We consider weighted generating functions of trees where the weights are products of functions of the sizes of the subtrees. This work begins with the observation that three different communities, largely independently, found substantially the same result concerning these series. We unify these results with a common generalization. Next we use the insights of one community on the problems of another in two different ways. Namely, we use the differential equation perspective to find a number of new interesting hook length formulae for trees, and we use the body of examples developed by the combinatorial community to give quantum field theory toy examples with nice properties.
[도널드 커누스(Donald Knuth), Claude Opus 4.6이 미해결 조합론 문제를 해결한 과정을 논문으로 공개
도널드 커누스가 Claude Opus 4.6이 미해결 조합론 문제를 해결한 과정을 논문으로 공개했습니다. Claude는 31번의 Python 스크립트 실행과 자체 피드백 루프를 통해 해밀토니안 사이클 분해 문제를 해결했습니다. 커누스는 AI의 자동 연역과 창의적 문제 해결 능력에 대해 긍정적인 평가를 내렸습니다.
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the ! at the end is because the addresses are happy to participate
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--- me, explaining to my cat squeaks why the formula <addresses>! explains why the rate of expansion in the universe is slightly accelerating
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"""
your math only works when the number of addresses are small, by the time you account for routing and network effects that cause many of those writes to land back on existing addresses, the rate of expansion is more likely to fall on a curve plotted by n(n-1)/2
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--- squeaks, writely skeptical
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"""
your homonym puns are week and i really wanted to make a factorial joke this once!
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--- me, explaining to my cat squeaks why homonym puns don't work when you're having a vocal debate
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"""
i could have arranged for a better pun
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--- squeaks, getting too tired to finish the joke properly
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"""
and my jokes all landed where they were supposed to... nowhere
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--- me, finally understanding why derangement notation uses factorials
As part of the CWI thematic research semester programme Phase Transitions in Combinatorics, Algorithms and Probability (PhaseCAP), we organise a series of three colloquia in Amsterdam. Please register via the links below if you want to attend. Registration closes a week before the meeting or when capacity is reached.
Thursday, 2 April — PhaseP colloquium
13:30–14:00 Coffee reception
14:00–15:00 Christina Goldschmidt (Oxford): Stable trees
15:00–16:00 Tom Bohman (Carnegie Mellon): Notes on two-point concentration in random graphs
16:00–17:30 Drinks reception
Friday, 17 April — PhaseC colloquium
13:30–14:00 Coffee reception
14:00–15:00 Penny Haxell (Waterloo): Algorithms for Independent Transversals and Reconfiguration
15:00–16:00 Rob Morris (IMPA): Recent results in Ramsey theory
16:00–17:30 Drinks reception
Friday, 29 May — PhaseA colloquium
14:00–15:00 Leslie Goldberg (Oxford): Fundamental Instability of Backoff Protocols
15:00–16:00 Amin Coja-Oghlan (Dortmund): The cavity method
16:00–17:30 Drinks reception
Please feel free to share this announcement with colleagues who may be interested.
#combinatorics #probability #algorithms #amsterdam #phasetransitions #CWI
Ross Kang
Søren Fuglede Jørgensen
kipriyanovich
Aleph ω+4
Paul Balduf
sayzard
graeme fawcett