Aaron Lauve’s


Those pictures appearing on my welcome page? They all appear below… enjoy!

Mathematical Vignettes

Some images below borrowed under the creative commons license from WikiMedia

What is a square, really?
Cayley graphs for everyone
You're familiar with determinants,… how about quasideterminants?
What's special about this sequence?
It's “square free” (search for “1 0 2 1 2 0” in the link above)
Why do these shifted Fibonacci numbers sum to 1/89?
(and what other numbers can be so produced?)
Wait… aperiodic tilings!?
What's special about this number?

Longer Mathematical Pieces
Two stories from the theory of words
The combinatorics of pointed Hopf algebras
Hopf structures on the multiplihedra
Littlewood–Richardson rules from Hopf algebras
Revisiting Markoff's study of quadratic forms
Finding primitives via transfer of structure
A stable basis for QSym over Sym
Lagrange’s theorem for Species

Where was Aaron?
Hint:  on an island in the Isar
Hint:  google Buren
Hint:  near Týn Church
Hint:  you’ll have to ask me, it has vanished
Hint:  not a boathouse, but a boat-house
Hint:  near Chamonix–Mont Blanc
Hint:  on the “Ring Road”