748 citations · 839 across the 24 of their papers we have counts for
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Critical groups in harmonic abelian quotients
Mariia Vetluzhskikh, Dmitry Zakharov
A harmonic cover of graphs induces a surjective pushforward morphism on the critical groups.…
A matroidal perspective on the tropical Prym variety
Felix Röhrle, Dmitry Zakharov
We associate a matroid to a harmonic double cover of metric graphs. The matroid is a geometric interpretation of Zaslavsk…
Chip-firing on graphs of groups
Margaret Meyer, Dmitry Zakharov
We define the Laplacian matrix and the Jacobian group of a finite graph of groups. We prove analogues of the matrix tree theorem and the class number formula for the order of the J…
The Prym variety of a dilated double cover of metric graphs
Arkabrata Ghosh, Dmitry Zakharov
We calculate the volume of the tropical Prym variety of a harmonic double cover of metric graphs having non-trivial dilation. We show that the tropical Prym variety behaves discont…
The tropical -gonal construction
Felix Röhrle, Dmitry Zakharov
We give a purely tropical analogue of Donagi's -gonal construction and investigate its combinatorial properties. The input of the construction is a harmonic double cover of an $…
Zeta functions of edge-free quotients of graphs
Dmitry Zakharov
We consider the Ihara zeta function and Artin-Ihara -function of the quotient graph of groups , where is a group acting on a finite graph with trivial…