14 citations · 32 across the 21 of their papers we have counts for
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math.DS2005
Periodic Orbits of Billiards on an Equilateral Triangle
Andrew M. Baxter, Ron Umble
We give a complete solution of the following problem: Find, classify and count the (classes of) periodic orbits on an equilateral triangle. We prove that Fagnano's period 3 orbit i…
math.AT2005
Matrads, Biassociahedra and A_{\infty}-Bialgebras
Samson Saneblidze, Ronald Umble
We introduce the notion of a matrad M = {M_{n,m}} whose submodules M_{*,1} and M_{1,*} are non-Sigma operads. We define the free matrad H_{\infty} generated by a singleton in each…
math.AT2005★ 1 cited
Structure Relations in Special A_\infty-bialgebras
Ronald Umble
We compute the structure relations in special A_\infty-bialgebras whose operations are limited to those defining the underlying A_\infty-(co)algebra substructure. Such bialgebras a…