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Fordham, S. Blake

doi:10.1023/a:1024971818319

Cited by 31 publications

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“…To calculate restricted rotation distance, we use the methods of Fordham [15]. His methods were designed to calculate word length exactly in Thompson's group F with respect to the generating set {x 0 , x −1 0 , x 1 , x −1 1 }, and give minimal length representatives of a word with respect to that generating set.…”

Section: Background and Definitionsmentioning

confidence: 99%

“…A primary result of Fordham [15] is that the word length |w| in Thompson's group F with respect to the standard finite generating set can be calculated by classifying node pairs into those seven types and summing the totals from the Table 1. Note that the first node pair is always of type (L 0 , L 0 ) and adds weight 0, and the single L 0 in each tree must necessarily be paired, so the caret type L 0 is not listed in Table 1.…”

Section: Background and Definitionsmentioning

confidence: 99%

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Distributions of restricted rotation distances

Cleary

Nadeem

2022

Art Discrete Appl. Math.

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Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a single rotation. There are no known efficient algorithms to compute rotation distance between trees and thus distances in rotation graphs. Limiting the allowed locations of where rotations are permitted gives rise to a number of notions related to rotation distance. Allowing rotations at a minimal such set of locations gives restricted rotation distance. There are linear-time algorithms to compute restricted rotation distance, where there are only two permitted locations for rotations to occur. The associated restricted rotation graph has an efficient distance algorithm. There are linear upper and lower bounds on restricted rotation distance with respect to the sizes of the reduced tree pairs. Here, we experimentally investigate the expected restricted rotation distance between two trees selected at random of increasing size and find that it lies typically in a narrow band well within the earlier proven linear upper and lower bounds.

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Section: Background and Definitionsmentioning

confidence: 99%

Section: Background and Definitionsmentioning

confidence: 99%

Distributions of restricted rotation distances

Cleary

Nadeem

2022

Art Discrete Appl. Math.

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Thompson’s Group F

Bonanome

Dean

2018

Compact Textbooks in Mathematics

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Computational Explorations in Thompson’s Group F

Burillo¹,

Cleary

Wiest

Trends in Mathematics

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Here we describe the results of some computational explorations in Thompson's group F . We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

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Cited by 31 publications

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Distributions of restricted rotation distances

Distributions of restricted rotation distances

Thompson’s Group F

Computational Explorations in Thompson’s Group F

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