@article{600b24f806ec4375a345c1ad479b22e3,
title = "Statistics of partial permutations via Catalan matrices",
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.",
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",
author = "Cheng, {Yen Jen} and Eu, {Sen Peng} and Hsu, {Hsiang Chun}",
note = "Funding Information: Y.-J. Cheng is partially supported by MOST 111-2811-M-A49-537-MY2 , S.-P. Eu is partial supported by MOST 110-2115-M-003-011-MY3 and H.-C. Hsu is partially supported by MOST 110-2115-M-032-004-MY2 . Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2023",
month = feb,
doi = "10.1016/j.aam.2022.102451",
language = "English",
volume = "143",
journal = "Advances in Applied Mathematics",
issn = "0196-8858",
publisher = "Academic Press Inc.",
}