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Abstract Let π n be a uniformly chosen random permutation on [ n ]. Using an analysis of the probability that two overlapping consecutive k -permutations are order isomorphic, we show that the expected number of distinct consecutive patterns of all lengths k ∈ {1, 2,…, n } in π n is n 2 2 ( 1 - o ( 1 ) ) {{{n^2}} \over 2}\left( {1 - o\left( 1 \right)} \right) as n → ∞. This exhibits the fact that random permutations pack consecutive patterns near-perfectly.
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This content will become publicly available on January 1, 2026
The degree of a tropical root surface of type A
We prove that the tropical surface of the root system A_{n−1} has degree n(n − 1)(n − 2)/2.
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- Award ID(s):
- 2154279
- PAR ID:
- 10523714
- Publisher / Repository:
- Mathematical Sciences Publishers
- Date Published:
- Journal Name:
- Orbita Mathematicae
- Volume:
- 2
- Issue:
- 1
- ISSN:
- 2993-6144
- Page Range / eLocation ID:
- 33 to 42
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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