17 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Errata and Addenda to Mathematical Constants
We humbly and briefly offer corrections and supplements to Mathematical
Constants (2003) and Mathematical Constants II (2019), both published by
Cambridge University Press. Comments are always welcome.Comment: 162 page
Free subgroups of free products and combinatorial hypermaps
We derive a generating series for the number of free subgroups of finite
index in by using a connection between
free subgroups of and certain hypermaps (also known as ribbon graphs
or "fat" graphs), and show that this generating series is transcendental. We
provide non-linear recurrence relations for the above numbers based on
differential equations that are part of the Riccati hierarchy. We also study
the generating series for conjugacy classes of free subgroups of finite index
in , which correspond to isomorphism classes of hypermaps. Asymptotic
formulas are provided for the numbers of free subgroups of given finite index,
conjugacy classes of such subgroups, or, equivalently, various types of
hypermaps and their isomorphism classes.Comment: 27 pages, 3 figures; supplementary SAGE worksheets available at
http://sashakolpakov.wordpress.com/list-of-papers
On Minimum Average Stretch Spanning Trees in Polygonal 2-trees
A spanning tree of an unweighted graph is a minimum average stretch spanning
tree if it minimizes the ratio of sum of the distances in the tree between the
end vertices of the graph edges and the number of graph edges. We consider the
problem of computing a minimum average stretch spanning tree in polygonal
2-trees, a super class of 2-connected outerplanar graphs. For a polygonal
2-tree on vertices, we present an algorithm to compute a minimum average
stretch spanning tree in time. This algorithm also finds a
minimum fundamental cycle basis in polygonal 2-trees.Comment: 17 pages, 12 figure