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Creators/Authors contains: "Berman, Yosef"

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  1. ; ; ; ; ; ; ; ; (, Applied Mathematics and Computation)
    Free, publicly-accessible full text available January 1, 2027
  2. ; ; ; ; (, Journal of Symbolic Computation)
    Free, publicly-accessible full text available May 1, 2026
  3. ; (, The Electronic Journal of Combinatorics)
    We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern counts, both in terms of a permutation and in terms of its image under the fundamental bijection. We use these enumerations to resolve the question of characterizing so-called "shallow" permutations, whose depth (equivalently, disarray/displacement) is minimal with respect to length and reflection length. We present this characterization in several ways, including vincular patterns, mesh patterns, and a new object that we call "arrow patterns." Furthermore, we specialize to characterizing and enumerating shallow involutions and shallow cycles, encountering the Motzkin and large Schröder numbers, respectively. 
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