30 citations · 292 across the 71 of their papers we have counts for
5 papers · 1 filter
Growth in free groups (and other stories)
Igor Rivin
We start by studying the distribution of (cyclically reduced) elements of the free groups with respect to their abelianization. We derive an explicit generating function, and a lim…
Simple cycles
Igor Rivin
We obtain sharp bounds for the number of n-cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be im…
Simple curves on surfaces
Igor Rivin
We show that the number of simple closed geodesics of length bounded by L on a hyperbolic surface of genus g with c cusps and b boundary components grows roughly like L^{6g+2b+2c-6…
On some extremal problems in graph theory
Dmitry Jakobson, Igor Rivin
In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs…
Combinatorial optimization in geometry
Igor Rivin
We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of…