@peterkagey.com - Peter Kagey

17 Apr 2026 14:56 +0000

Triangle of numbers of partitions of n with total number of odd parts equal to k from {0,...,n}. [contains quote post or other embedded content]

13 Apr 2026 14:41 +0000

Triangle T(n,d) read by rows: Number of ascent sequences of length n with d zeros. [contains quote post or other embedded content]

08 Apr 2026 16:01 +0000

I'm not sure I can explain it, but this is @motivickyle.bsky.social. [contains quote post or other embedded content]

21 Mar 2026 12:05 +0000

Hey! That’s the one in the profile picture! [contains quote post or other embedded content]

15 Mar 2026 18:44 +0000

Number T(n,k) of entries in the k-th cycles of all permutations of [n] when cycles are ordered by decreasing lengths (and increasing smallest elements); triangle T(n,k), n>=1, 1<=k<=n, read by rows. [contains quote post or other embedded content]

13 Mar 2026 23:20 +0000

Lately, I've been assigning my upper division math students "Choice Exercises" as a part of their homework assignments, where they get to choose from several options. When I taught Abstract Algebra in fall 2024, I asked students to say which problem was their favorite, which I've recorded here. https://peterkagey.com/blog/2026/03/favorite_problems_4170/

10 Mar 2026 16:51 +0000

Given reports that Americans buy SUVs in part because the other cars on the road are big, it surprised me that "The likelihood that someone gets into a fatal collision while traveling to and from work [is] higher if they drive a heavy SUV or pickup truck with big blind spots instead of a […] sedan." https://www.bloomberg.com/news/articles/2026-03-10/how-deadly-are-us-roads-it-depends-on-how-you-count-traffic-fatalities

08 Mar 2026 23:24 +0000

The number of non-equivalent distinguishing coloring partitions of the path on n vertices (n>=1) with exactly k parts (k>=1). Regular triangle read by rows: the rows are indexed by n, the number of vertices of the path, and the columns are indexed by k, the number of parts. [contains quote post or other embedded content]

05 Mar 2026 18:38 +0000

Check out @fdecomite.bsky.social’s incredible shelf based on Squaring the Square! [contains quote post or other embedded content]

27 Feb 2026 16:27 +0000

Inspired by @robinhouston.mathstodon.xyz.ap.brid.gy's G4G16 gift of tetragonal disphenoidal blocks, I've made some magnetized versions, which are satisfyingly click-y! [contains quote post or other embedded content]

25 Feb 2026 04:01 +0000

Triangle read by rows: T(n,k) = number of step shifted (decimated) sequence structures of length n using exactly k different symbols. [contains quote post or other embedded content]

22 Feb 2026 19:33 +0000

I wrote a blog post about my G4G16 gift. If you want a copy of your own, download and print the files! https://peterkagey.com/blog/2026/02/G4G16/

14 Jan 2026 19:06 +0000

Three podcasts that I loved that have since stopped releasing new episodes, but which I wish more people knew about. – Hakai Magazine Audio Edition – Ox Tales (by the Oxford Symposium on Food and Cookery) – 70 Over 70 (by Pineapple Street Studios) Please recommend defunct podcasts to me too!

27 Dec 2025 23:51 +0000

I wrote about the postcard I designed for the 2025 plotter postcard exchange #ptpx on my blog, based on a potato-based game that M.C. Escher used to play with his kids. https://peterkagey.com/blog/2025/12/potato_printing/

11 Dec 2025 18:32 +0000

Don Knuth just published OEIS sequence: "A391478: T(m,n) is the number of Hamiltonian cycles on an m×n torus where each step goes north (N), east (E), or northeast (NE), with 2 ≤ n ≤ m." It references three sequences, two of which are sequences I published in 2019! https://oeis.org/A391478

27 Nov 2025 17:01 +0000

I wrote a blog post about human polyhedra, which truly *embodies* mathematics. https://peterkagey.com/blog/2025/11/human_rd/

17 Nov 2025 06:38 +0000

In October 2014, a few months out of college, I made my first web app so users could submit examples of constructions of upper bounds for a graph theory problem. This last week, I've updated it to make it more mobile-friendly and colorful! Try it out and see if you can improve any of the bounds! https://peterkagey.com/apps/square_game/

13 Nov 2025 01:20 +0000

Check out my new blog post on a prototype shelf that I designed and made out of cardboard based on the "squaring the square" problem, which asks if you can partition a square into smaller squares all of different sizes. (You can!) Come for the photos, stay for the 3D model! https://peterkagey.com/blog/2025/11/squaring_the_shelf/

11 Nov 2025 23:28 +0000

I got a shoutout in the 245th edition of Carnival of Mathematics! https://www.theoremoftheday.org/SpecialEvents/CoM245.html

05 Nov 2025 22:21 +0000

Looks like #plotparty postcards have landed in mailboxes! Read my new blog post about the cards I designed. [contains quote post or other embedded content]

28 Oct 2025 02:47 +0000

Triangle T(m,n) giving of number of steps in the Euclidean algorithm for gcd(m,n) with 0<=m