Tower Tableaux
Olcay Co\c{s}kun, M\"uge Ta\c{s}k{\i}n

TL;DR
This paper introduces tower diagrams, a new combinatorial object, along with an algorithm to slide words onto these diagrams, establishing a bijection with permutations and a test for reducibility.
Contribution
The paper presents the novel concept of tower diagrams, an algorithm for sliding words, and a bijection with permutations, advancing combinatorial and permutation theory.
Findings
Algorithm is well-defined only for reduced words
Bijection between tower diagrams and permutations established
Algorithm serves as a reducibility test
Abstract
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only for reduced words which makes the algorithm a test for reducibility. Using the algorithm, a bijection between tower diagrams and finite permutations is obtained and it is shown that this bijection specializes to a bijection between certain labellings of a given tower diagram and reduced expressions of the corresponding permutation.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · semigroups and automata theory · Advanced Algebra and Logic
