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Keywords = permutation tableau

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12 pages, 336 KB  
Article
Marking Algorithms in Permutation Tableaux and Transformations on Linked Partitions
by Carol Jian Wang and Meryl Nan Wang
Mathematics 2025, 13(8), 1335; https://doi.org/10.3390/math13081335 - 19 Apr 2025
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Abstract
In this paper, we focus on the internal structural characteristics of permutation tableaux and their correspondence with linked partitions. We begin by introducing new statistics for permutation tableaux, designed to thoroughly describe various positional relationships among the topmost 1s and the rightmost restricted [...] Read more.
In this paper, we focus on the internal structural characteristics of permutation tableaux and their correspondence with linked partitions. We begin by introducing new statistics for permutation tableaux, designed to thoroughly describe various positional relationships among the topmost 1s and the rightmost restricted 0s. Subsequently, we develop two marking algorithms for permutation tableaux, each from the perspective of columns and rows. Additionally, we introduce tugging and rebound transformations, which elucidate the generative relationship from original partitions to linked partitions. As a result, we demonstrate that the construction of these two marking algorithms in permutation tableaux provides a straightforward method for enumerating the crossing number and nesting number of the corresponding linked partitions. Full article
(This article belongs to the Section A: Algebra and Logic)
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