43 citations · 163 across the 20 of their papers we have counts for
4 papers · 1 filter
Matrix-tree theorem for cohomological electrical networks
Pavlo Pylyavskyy, Svetlana Shirokovskikh, Mikhail Skopenkov
We introduce a new type of boundary condition for electrical networks by specifying a cohomology class on the underlying cell complex. As special and limiting cases, we recover the…
Superport networks
Pavlo Pylyavskyy, Svetlana Shirokovskikh, Mikhail Skopenkov
We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the…
The boundary value problem for discrete analytic functions
Mikhail Skopenkov
This paper is on further development of discrete complex analysis introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We consider a graph lying in the complex plane and…
Tiling by rectangles and alternating current
M. Prasolov, M. Skopenkov
This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-cur…