Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Split a list at its lefttoright maxima
ResourceFunction["DescendingSublists"][list] makes sublists of list starting at its lefttoright maxima. 
Split a permutation given as a list into sublists starting at its lefttoright maximum:
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The input does not have to be a permutation:
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Flatten to get back to the original list:
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Here is a larger example:
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Each sublist starts from its maximum:
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The first elements are increasing:
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The sublists of s1 can be thought of as cycle notation for the permutation, but with a different canonical form than the Wolfram Language default, where each sublist starts with its minimum:
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