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September 24, 2026

Binomial Coefficient Coincidences

Posted by John Baez

These seven equations between binomial coefficients are ‘coincidences’ — they aren’t among the four known infinite families of such equations:

(162)=(103)=120 \binom{16}{2} = \binom{10}{3} = 120

(212)=(104)=210 \binom{21}{2} = \binom{10}{4} = 210

(562)=(223)=1540 \binom{56}{2} = \binom{22}{3} = 1540

(782)=(146)=3003 \binom{78}{2} = \binom{14}{6} = 3003

(1202)=(363)=7140 \binom{120}{2} = \binom{36}{3} = 7140

(1532)=(195)=11628 \binom{153}{2} = \binom{19}{5} = 11628

(2212)=(178)=24310 \binom{221}{2} = \binom{17}{8} = 24310

Continue reading “Binomial Coefficient Coincidences” …
Posted at 9:37 PM UTC | Permalink | Followups (5)

September 8, 2026

The E6 Root Polytope

Posted by John Baez

I’ve been thinking about the exceptional Lie algebra E6, as a spinoff of my project on E7, so I want to get a good mental picture of the E6 root polytope. This is 6-dimensional polytope with remarkable symmetry.

Continue reading “The E6 Root Polytope” …
Posted at 6:20 PM UTC | Permalink | Post a Comment