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Properties of the Edelman-Greene bijection. (English) Zbl 1430.05132
Summary: P. Edelman and C. Greene [Contemp. Math. 34, 155–162 (1984; Zbl 0562.05008)] constructed a bijective correspondence between reduced words of the reverse permutation and standard Young tableaux. We prove that for any reduced word the shape of the region of the insertion tableau containing the smallest possible entries evolves exactly as the upper-left component of the permutation’s (Rothe) diagram. Properties of the Edelman-Greene bijection restricted to 132-avoiding and 2143-avoiding permutations are presented. We also consider the Edelman-Greene bijection applied to non-reduced words.
MSC:
05E10 Combinatorial aspects of representation theory
05A05 Permutations, words, matrices
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