97 citations · 431 across the 34 of their papers we have counts for
7 papers · 1 filter
The Markov chain tree theorem and the state reduction algorithm in commutative semirings
Buket Benek Gursoy, Steve Kirkland, Oliver Mason +1
We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal a…
On sets of eigenvalues of matrices with prescribed row sums and prescribed graph
Gernot Michael Engel, Hans Schneider, Sergei Sergeev
Motivated by a work of Boros, Brualdi, Crama and Hoffman, we consider the sets of (i) possible Perron roots of nonnegative matrices with prescribed row sums and associated graph, a…
Weak CSR expansions and transience bounds in max-plus algebra
Glenn Merlet, Thomas Nowak, Sergei Sergeev
This paper aims to unify and extend existing techniques for deriving upper bounds on the transient of max-plus matrix powers. To this aim, we introduce the concept of weak CSR expa…
Generalizations of Bounds on the Index of Convergence to Weighted Digraphs
Glenn Merlet, Thomas Nowak, Hans Schneider +1
We study sequences of optimal walks of a growing length, in weighted digraphs, or equivalently, sequences of entries of max-algebraic matrix powers with growing exponents. It is kn…
On the dimension of max-min convex sets
Viorel Nitica, Sergei Sergeev
We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show t…
On the max-algebraic core of a nonnegative matrix
Peter Butkovic, Hans Schneider, Sergei Sergeev
The max-algebraic core of a nonnegative matrix is the intersection of column spans of all max-algebraic matrix powers. Here we investigate the action of a matrix on its core. Being…
Tropical convexity over max-min semiring
Viorel Nitica, Sergei Sergeev
This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an accoun…