Abstract
A generalized Catalan matrix (an,k)n,k≥0 is generated by two seed sequences s=(s0,s1,…) and t=(t1,t2,…) together with a recurrence relation. By taking sℓ=2ℓ+1 and tℓ=ℓ2 we can interpret an,k as the number of partial permutations, which are n×n 0,1-matrices of k zero rows with at most one 1 in each row or column. In this paper we prove that most of fundamental statistics and some set-valued statistics on permutations can also be defined on partial permutations and be encoded in the seed sequences. Results on two interesting permutation families, namely the connected permutations and cycle-up-down permutations, are also given.
Original language | English |
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Article number | 102451 |
Journal | Advances in Applied Mathematics |
Volume | 143 |
DOIs | |
Publication status | Published - 2023 Feb |
Keywords
- Catalan matrix
- Connected permutation
- Cycle
- Cycle-up-down permutation
- Descent
- Excedance
- Fixed point
- Inversion
- Partial permutation
- Permutation
- Right-to-left minimum
- Set-valued statistic
- Statistic
ASJC Scopus subject areas
- Applied Mathematics