Consecutive patterns in restricted permutations and involutions

Autor: Barnabei, M., Bonetti, F., Castronuovo, N., Silimbani, M.

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol. 21 no. 3 , Combinatorics (June 5, 2019) dmtcs:5175

It is well-known that the set $\mathbf I_n$ of involutions of the symmetric group $\mathbf S_n$ corresponds bijectively - by the Foata map $F$ - to the set of $n$-permutations that avoid the two vincular patterns $\underline{123},$ $\underline{132}.$

Externí odkaz: http://arxiv.org/abs/1902.02213

Italian versions of the optimal screening for Prediction of Referral and Outcome Yellow Flag (OSPRO-YF) and the Örebro Musculoskeletal pain screening questionnaire (ÖMPQ-21) and their short forms, in patients with low back pain: Cross-cultural adaptation, reliability and validity.

Autor: Bonetti F; University of Rome Tor Vergata, Rome, Italy; Physioup Physiotherapy Practice, Rome, Italy. Electronic address: fra.bonetti@me.com., Angilecchia D; Department of Medicine and Health Science 'Vincenzio Tiberio', University of Molise, Campobasso, Italy; Rehabilitation Service-ASL, Bari, Italy., Agostini A; University of Rome Tor Vergata, Rome, Italy; Pain Unit. Santa Maria Maddalena Hospital. Advance Algology Research, via Gorizia, 2, 45030, Occhiobello, RO, Italy., Marighetto P; University of Rome Tor Vergata, Rome, Italy; Private Physiotherapy Practice, Castello di Godego, TV, Italy., Minnucci S; University of Rome Tor Vergata, Rome, Italy., Giglioni G; University of Rome Tor Vergata, Rome, Italy; Department of Rehabilitation, Asl Roma3, Rome, Italy., Pellicciari L; IRCCS Istituto delle Scienze Neurologiche di Bologna, Bologna, Italy., Chiarotto A; Department of General Practice, Erasmus MC, University Medical Center, Rotterdam, the Netherlands.

Publikováno v: Musculoskeletal science & practice [Musculoskelet Sci Pract] 2024 Nov; Vol. 74, pp. 103206. Date of Electronic Publication: 2024 Oct 21.

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The descent statistic over 123-avoiding permutations

Autor: Barnabei, M., Bonetti, F., Silimbani, M.

We exploit Krattenthaler's bijection between 123-avoiding permutations and Dyck paths to determine the Eulerian distribution over the set $S_n(123)$ of 123-avoiding permutations in $S_n$. In particular, we show that the descents of a permutation corr

Externí odkaz: http://arxiv.org/abs/0910.0963

Restricted involutions and Motzkin paths

Autor: Barnabei, M., Bonetti, F., Silimbani, M.

We show how a bijection due to Biane between involutions and labelled Motzkin paths yields bijections between Motzkin paths and two families of restricted involutions that are counted by Motzkin numbers, namely, involutions avoiding 4321 and 3412. As

Externí odkaz: http://arxiv.org/abs/0812.0463