Mastodawn

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

Ordered Ramsey and Turán numbers of alternating paths and their variants

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.

arXiv.org

Aleph ω+4 Mar 14

https://norvig.com/atoms.html

No wonder #combinatorics is hard!
#mathematics #maths #math

Paul Balduf Mar 14

#paperOfTheDay for Friday was "Tree hook length formulae, Feynman rules and B-series" from 2014. This is a #mathematics paper, more specifically #combinatorics . It deals with rooted trees, that is, connected graphs without cycles and with one distinguished vertex. For a given vertex, the subtree is the unique tree that is obtained by taking the vertex as a root, and discarding everything that was above the new root in the original tree. One then defines a "hook length formula" to be a mapping from rooted trees to some ring, which is given by evaluating some function on each subtree and multiplying the result. The classical example is the "tree factorial", where the function on the subtree is the number of vertices, so that the entire tree evaluates to the product of the number of vertices of all subtrees (which equals the ordinary factorial if the tree is a path). This construction might seem obscure, but it is widely used, and the present paper makes an effort to unify these results. For example, Runge-Kutta schemes for numerical integration of differential equations have an algebraic form called B-series, which essentially is a hook length formula. Also, renormalization of divergent subdiagrams in #quantumFieldTheory has this structure. The present paper discovers various new closed-form expressions for hook length formulae. From the perspective of QFT, what they do is invent new toy model Feynman rules that give rise to nice closed-form Green functions. I find this quite useful for a systematic qualitative understanding of QFT, even if these particular Feynman rules don't have an immediate physical interpretation. https://arxiv.org/abs/1412.6053

Tree hook length formulae, Feynman rules and B-series

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.

arXiv.org

sayzard Mar 3

[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.

https://news.hada.io/topic?id=27176

#ai #computerscience #combinatorics #claudopus #donaldknuth

도널드 커누스(Donald Knuth), Claude Opus 4.6이 미해결 조합론 문제를 해결한 과정을 논문으로 공개

<h4>핵심 요약</h4> <ul> <li>'컴퓨터 프로그래밍의 예술(TAOCP)'의 저자인 컴퓨터 과학자 도널드 커누스가 최신 AI 모델 'Claude Opus 4.6'이 자...

GeekNews

graeme fawcett Feb 27

"""
the ! at the end is because the addresses are happy to participate
"""
--- me, explaining to my cat squeaks why the formula <addresses>! explains why the rate of expansion in the universe is slightly accelerating

===

"""
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
"""
--- squeaks, writely skeptical

===

"""
your homonym puns are week and i really wanted to make a factorial joke this once!
"""
--- me, explaining to my cat squeaks why homonym puns don't work when you're having a vocal debate

===

"""
i could have arranged for a better pun
"""
--- squeaks, getting too tired to finish the joke properly

===

"""
and my jokes all landed where they were supposed to... nowhere
"""
--- me, finally understanding why derangement notation uses factorials

#physics #combinatorics #mathematics

Ross Kang Feb 26

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

Registration: https://www.cwi.nl/en/research/algorithms-and-complexity/events/registration-phasecap-probability-plenary-talks-thursday-2-april-2026/

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

Registration: https://www.cwi.nl/en/events/research-semester-programmes/phasecap-phase-transitions-in-combinatorics-algorithms-probability/17-april-2026-phasecap-combinatorics-plenary-talks/

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

Registration: https://www.cwi.nl/en/events/research-semester-programmes/phasecap-phase-transitions-in-combinatorics-algorithms-probability/registration-phasecap-algorithms-plenary-talks-friday-29-may-2026/

Please feel free to share this announcement with colleagues who may be interested.

#combinatorics #probability #algorithms #amsterdam #phasetransitions #CWI

Registration PhaseP Plenary talks Thursday 2 April 2026

Paul Balduf Feb 23

In May, there will be a Colloquium on #combinatorics in London! #mathematics https://2dcic.github.io/speakers.html

Speakers

2026 Colloquia in Combinatorics

Ross Kang Feb 17

That was fun! Here's hoping that it won't be another 17 years before the next time I am at the Combinatorial Theory Seminar here...

#combinatorics #oxford #nostalgia

Centre for Population Change Feb 16

📑 A new paper by CPC-CG members introduces the first method that can predict how many relatives of any kind a person is likely to have at different points in their life, and how likely each outcome is:
https://www.demographic-research.org/articles/volume/54/9

#demography #kinship #mathematicaldemography #populationstudies #lifeCourse #mortality #fertility #probability #matrixalgebra #combinatorics #convolution #kin #familyStructure #analyticModel #populationResearch #population #family #familystructures #demographicforecasting

csamsanm Feb 16

🎉🥳 I won today's Hackenbush game playing as 🔴 Red!

#combinatorics #gametheory #combinatorialgames

Play Hackenbush at: https://hackenbush.vercel.app/

Hackenbush - Daily Combinatorial Game

Play Hackenbush online, the classic combinatorial game by John Conway. Learn game theory while playing this strategic mathematical game. Free daily puzzles!

Hackenbush Game