2 citations · 4 across the 5 of their papers we have counts for
6 papers
Some Aspects of Higher Continued Fractions
Etan Basser, Nicholas Ovenhouse, Anuj Sakarda
We investigate some properties of the higher continued fractions defined recently by Musiker, Ovenhouse, Schiffler, and Zhang. We prove that the maps defining the higher continued…
-Rational and -Real Binomial Coefficients
John Machacek, Nicholas Ovenhouse
We consider -binomial coefficients built from the -rational and -real numbers defined by Morier-Genoud and Ovsienko in terms of continued fractions. We establish versions…
-Rationals and Finite Schubert Varieties
Nicholas Ovenhouse
The classical -analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give -analogues of rational numbers. Some combinatorial interpretations are…
Discrete Dynamical Systems From Real Valued Mutation
John Machacek, Nicholas Ovenhouse
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated w…
Non-Commutative Integrability of the Grassmann Pentagram Map
Nicholas Ovenhouse
The pentagram map is a discrete integrable system first introduced by Schwartz in 1992. It was proved to be intregable by Schwartz, Ovsienko, and Tabachnikov in 2010. Gekhtman, Sha…
Log-Canonical Coordinates for Poisson Brackets and Rational Changes of Coordinates
John Machacek, Nicholas Ovenhouse
Goodearl and Launois have shown that for a log-canonical Poisson bracket on affine space there is no rational change of coordinates for which the Poisson bracket is constant. Our m…