R. Umble

activity

20002022

most citedA Diagonal on the Associahedra

14 citations · 32 across the 21 of their papers we have counts for

collaborators

22 papers

math.AT2022★ 2 cited

Comparing Diagonals on the Associahedra

Samson Saneblidze, Ronald Umble

We prove that the formula for the diagonal approximation $Δ_{K}$ on J. Stasheff's $n$ -dimensional associahedron $K_{n + 2}$ derived by the current authors in 2004 agrees with the "ma…

math.CO2021

Computing the Dimension of a Bipartition Matrix

Dawson Freeman, Ronald Umble

The dimension of a bipartition matrix (BPM) is the sum of the dimensions of its indecomposable factors. The dimension of an indecomposable BPM is the sum of its row, column, and en…

math.AT2021

Framed Matrices and $A_{\infty}$ -Bialgebras

Samson Saneblidze, Ronald Umble

We complete the construction of the biassociahedra $K K$ , construct the free matrad $H_{\infty}$ , realize $H_{\infty}$ as the cellular chains of $K K,$ and define…

math.DS2019

Periodic Orbits on Obtuse Edge Tessellating Polygons

Benjamin R. Baer, Faheem Gilani, Zhigang Han +1

A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period…

math.AT2018

An $A_{\infty}$ -coalgebra Structure on a Closed Compact Surface

Quinn Minnich, Ronald Umble

Let $P$ be an $n$ -gon with $n \geq 3.$ There is a formal combinatorial $A_{\infty}$ -coalgebra structure on cellular chains $C_{*} (P)$ with non-vanishing higher order structure when $n\ge…

math.HO2014

Constructing the fixed point of a non-isometric plane similarity

Zhigang Han, Ron Umble

We present an algorithm for constructing the fixed point of a general non-isometric similarity of the plane.