36 citations · 51 across the 9 of their papers we have counts for
9 papers
Functional degrees and arithmetic applications III: Beyond Prime Exponent
Pete L. Clark, Uwe Schauz
Continuing our work on group-theoretic generalizations of the prime Ax-Katz Theorem, we give a lower bound on the -adic divisibility of the cardinality of the set of simultaneou…
Functional degrees and arithmetic applications II: The Group-Theoretic Prime Ax-Katz Theorem
Pete L. Clark, Uwe Schauz
We give a version of Ax-Katz's -adic congruences and Moreno-Moreno's -weight refinement that holds over any finite commutative ring of prime characteristic. We deduce this fr…
The Largest Possible Finite Degree of Functions between Commutative Groups
Uwe Schauz
We consider maps between commutative groups and their functional degrees. These degrees are defined based on a simple idea -- the functional degree should decrease if a discrete de…
Orientations of 1-Factorizations and the List Chromatic Index of Small Graphs
Uwe Schauz
As starting point, we formulate a corollary to the Quantitative Combinatorial Nullstellensatz. This corollary does not require the consideration of any coefficients of polynomials,…
The Moments of Lévy's area using a sticky shuffle Hopf algebra
Robin Hudson, Uwe Schauz, Wu Yue
Lévy's stochastic area for planar Brownian motion is the difference of two iterated integrals of second rank against its component one-dimen\-sional Brownian motions. Such iterated…
Moments of quantum Lévy areas using sticky shuffle Hopf algebras
Robin Hudson, Uwe Schauz, Yue Wu
We study a family of quantum analogs of Lévy's stochastic area for planar Brownian motion depending on a variance parameter which deform to the classical Lévy area as $σ\…
The Tournament Scheduling Problem with Absences
Uwe Schauz
We study time scheduling problems with allowed absences as a new kind of graph coloring problem. One may think of a sport tournament where each player (each team) is permitted a ce…
Classification of Polynomial Mappings Between Commutative Groups
Uwe Schauz
Some polynomials with rational coefficients give rise to well defined maps between cyclic groups, , . More generally, there…
Algebraic proof of Brooks' theorem
Jan Hladký, Daniel Král', Uwe Schauz
We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more ge…