17 research outputs found

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Errata and Addenda to Mathematical Constants

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    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

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    We derive a generating series for the number of free subgroups of finite index in Δ+=ZpZq\Delta^+ = \mathbb{Z}_p*\mathbb{Z}_q by using a connection between free subgroups of Δ+\Delta^+ 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 Δ+\Delta^+, 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

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    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 nn vertices, we present an algorithm to compute a minimum average stretch spanning tree in O(nlogn)O(n \log n) time. This algorithm also finds a minimum fundamental cycle basis in polygonal 2-trees.Comment: 17 pages, 12 figure
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