RE: https://mastoxiv.page/@arXiv_mathCO_bot/115904052353835071

Here is the second 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.

The first manuscript already came out a couple months earlier (https://arxiv.org/abs/2510.17981).

Both have made serious progress in serious Erdős problems.

#combinatorics #remoteconferences #graphtheory #extremalcombinatorics #erdős

“I feel that many women, especially in India, might not know what exactly having a career in maths actually means or even that they can pursue a career in this field. I believe it is important to tell them that this is an option.” - Nishu Kumari

➡️https://hermathsstory.eu/nishu-kumari/

#Academia #Combinatorics #Europe #Mathematics #PhD #Postdoc

#ThisWeeksFiddler, 20260123
This week the #puzzle is: Bingo! #statistics #probabilities #combinatorics #counting #coding #program #montecarlo A game of bingo typically consists of a 5-by-5 grid with 25 total squares. Each square (except for the center square) contains a number. When a square’s number is called, you place a marker on that square. The goal is to get […]

https://stuff.ommadawn.dk/2026/01/27/thisweeksfiddler-20260123/

And a more solid representation illustrates how the tiles fit together even better.

(4/n)

#tilingTuesday #math #3d #geometry #combinatorics

This 11-gon forms the surface.

(3/n) #tilingTuesday #math #3d #geometry #combinatorics

4 tiles form a module.

(2/n) #tilingTuesday #math #3d #geometry #combinatorics

Nicely twisted excerpt of a monohedral 11-gon tiling of a non-compact surface embedded in 𝑅³. (3 11-gons at every vertex)

The surface shows two periodic growth and the labeled dual edges of the tiling form a partial Cayley surface complex of the group:

G = ⟨ f₁, f₂, f₃, t₁, t₂, t₃, t₄ ∣ f₁², f₂², f₃², t₄³, t₁³, t₃⁶, (t₁t₄⁻¹)⁹, f₃t₂, t₁t₃t₂, (f₁t₁)², f₃t₃t₄⁻¹ ⟩

(1/n) #tilingTuesday #math #3d #geometry #combinatorics

#APLQuest 2014-06: Write a function that takes an integer vector representing the sides of a number of dice and returns a 2 column matrix of the number of ways each possible total of the dice can be rolled (see https://apl.quest/2014/6/ to test your solution and view ours). #APL #Probability #Combinatorics

Riffs and Rotes • Happy New Year 2026
• https://inquiryintoinquiry.com/2026/01/01/riffs-and-rotes-happy-new-year-2026/

There's a deep mathematical significance I see in the following structures, and I'm hoping one day to find a way to explain all the things I see there. Meanwhile, you may take them as an amusing diversion in recreational maths.

\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)

\( \begin{array}{llcl}
\text{Then} & 2026 & = & 2 \cdot 1013
\\
&& = & p_1 p_{170}
\\
&& = & p_1 p_{2 \cdot 5 \cdot 17}
\\
&& = & p_1 p_{p_1 p_3 p_7}
\\
&& = & p_1 p_{p_1 p_{p_2} p_{p_4}}
\\
&& = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}
\end{array} \)

No information is lost by dropping the terminal 1s. Thus we may write the following form.

\[ 2026 = p p_{p p_{p_p} p_{p_{p^p}}} \]

The article linked below tells how forms of that order correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2026 are shown in the next two Figures.

Riff 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/riff-2026-card.png

Rote 2026
• https://inquiryintoinquiry.com/wp-content/uploads/2026/01/rote-2026-card.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

cc: https://www.academia.edu/community/VBA6Qz
cc: https://www.researchgate.net/post/Riffs_and_Rotes_Happy_New_Year_2026

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

Monoid representations and partitions (Charlotte Aten at DU Algebra and Logic Seminar 2023)

https://videos.trom.tf/w/65QpmvUhdkwDhWmQHzzvFY

Bell numbers, the number of ways to partition a set of labeled elements https://janmr.com/posts/bell-numbers/ #math #combinatorics #bell #numbers

\[
\begin{aligned}
&\{\{k_1,k_2,k_3\}\} \\
&\{\{k_1,k_2\}, \{k_3\}\} \\
&\{\{k_1,k_3\}, \{k_2\}\} \\
&\{\{k_2,k_3\}, \{k_1\}\} \\
&\{\{k_1\}, \{k_2\}, \{k_3\}\} \\
\end{aligned}
\]

Advent of Tilings - Day 24

Happy Holidays, and best wishes for a 2026 filled with imagination, curiosity and discovery!

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 23.2

Another one rule wonder…

f₁t₁f₁t₂t₁⁻¹t₂

#math #geometry #3d #combinatorics #tiling #AdventOfTilings #TilingTuesday

Advent of Tilings - Day 23.1

Almost at the end we see the light through diamond and hexagon shaped tunnels of an infinite surface, again monohedrally tiled.

#math #geometry #3d #combinatorics #tiling #AdventOfTilings #TilingTuesday

Advent of Tilings - Day 22.2

It takes only one rule to get from single tile to cuboid

f₁f₂t₁t₂⁻¹t₁f₁t₁⁻¹

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 22.1

It is not always easy to find a symmetric tree, but keep it in a pot and you may be surprised by what it grows up to be.

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 21.2

The looping rules seem to reflect the strictness of the construction:

(f₂t₁t₂)²
(f₁t₁t₁)²

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 21.1

This tiling grows following a double pyramid shape that would make Djoser proud. Embeddable and monohedral.

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 20.2

The twist of the structure is accomplished by the rules:
(f₁t₁)² and f₁f₂t₂⁻¹t₁t₂t₂f₂t₂⁻¹ and (f₁f₂t₂⁻¹)³

#math #geometry #3d #combinatorics #tiling #AdventOfTilings

Advent of Tilings - Day 20.1

Adding a little twist of the necks in the surface of day 19, we can open the structure even more, while still keeping the concatenated CYAN edges straight. The tiling remains embeddable and monohedral.

#math #geometry #3d #combinatorics #tiling #AdventOfTilings