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- W2562127540 abstract "The register function (or Horton-Strahler number) of a binary tree is a well-known combinatorial parameter. We study a reduction procedure for binary trees which offers a new interpretation for the register function as the maximal number of reductions that can be applied to a given tree. In particular, the precise asymptotic behavior of the number of certain substructures (branches) that occur when reducing a tree repeatedly is determined. In the same manner we introduce a reduction for simple two-dimensional lattice paths from which a complexity measure similar to the register function can be derived. We analyze this quantity, as well as the (cumulative) size of an (iteratively) reduced lattice path asymptotically." @default.
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- W2562127540 date "2018-01-01" @default.
- W2562127540 modified "2023-09-25" @default.
- W2562127540 title "Reductions of binary trees and lattice paths induced by the register function" @default.
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- W2562127540 doi "https://doi.org/10.1016/j.tcs.2017.09.015" @default.
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