Explicit Enumeration of 321,Hexagon-Avoiding Permutations

2001/06/11 by Zvezdelina Stankova-Frenkel, Stankova-Frenkel, Zvezdelina, Julian West +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0106073

21 pages, 12 figures. submitted to Discrete Mathematics

arxiv created 2001/06/11 · openalex publication_date 2001/06/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The 321,hexagon-avoiding (321-hex) permutations were introduced and studied by Billey and Warrington in as a class of elements of S_n whose Kazhdan-Lusztig and Poincare polynomials and the singular loci of whose Schubert varieties have certain fairly simple and explicit descriptions. This paper provides a 7-term linear recurrence relation leading to an explicit enumeration of the 321-hex permutations. A complete description of the corresponding generating tree is obtained as a by-product of enumeration techniques used in the paper, including Schensted's 321-subsequences decomposition, a 5-parameter generating function and the symmetries of the octagonal patterns avoided by the 321-hex permutations.

Cited by

• Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
• Restricted permutations related to Fibonacci numbers and k-generalized Fibonacci numbers

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