We explore how the asymptotic structure of a random permutation of [n] with m
inversions evolves, as m increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. Our investigation begins
with exploring how the asymptotic structure of a random n-term weak integer composition of m evolves, as m increases from zero. The primary focus of our investigation
into compositions is establishing thresholds for the appearance and disappearance of
substructures, particularly the appearance and disappearance of consecutive composition patterns. We are then able to transfer the established composition threshold
to establish the thresholds for classical, consecutive or vincular permutation patterns
occurring within our random permutation model.
This thesis is based on the papers [12] and [13].
| Date of Award | 4 Jun 2025 |
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| Original language | English |
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| Awarding Institution | - University Of Strathclyde
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| Sponsors | EPSRC (Engineering and Physical Sciences Research Council) |
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| Supervisor | David Bevan (Supervisor) & Einar Steingrimsson (Supervisor) |
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