Restricted single or double signed patterns

2000/11/12 by Toufik Mansour, T. Mansour, Mansour, T.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0011072

13 pages, 1 table, 1 figure

arxiv created 2000/11/12 · openalex publication_date 2000/11/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E_n^r=\[τ]_a=(τ₁^(a₁),...,τ_n^(a_n))| τ∈ S_n, 1≤ a_i≤ r\ be the set of all signed permutations on the symbols 1,2,...,n with signs 1,2,...,r. We prove, for every 2-letter signed pattern [τ]_a, that the number of [τ]_a-avoiding signed permutations in E_n^r is given by the formula ∑_j=0ⁿ j!(r-1)^jn\choose j². Also we prove that there are only one Wilf class for r=1, four Wilf classes for r=2, and six Wilf classes for r≥ 3.

Related

• Wilf classification of three and four letter signed patterns
• New equivalences for pattern avoiding involutions
• Restricted permutations by patterns of type (2,1)
• Permutations containing and avoiding certain patterns
• Global patterns in signed permutations