Chu, H.V.Irmak, N.Miller, S.J.Szalay, L.Zhang, S.X.2025-12-242025-12-24202497831105968619783110621730978311076029397831106013299783110636734978311075534397831106601669783110753431978311078572297831113043732942-4801https://doi.org/10.1515/9783111395593-007https://hdl.handle.net/123456789/12754Inspired by the surprising relationship (due to A. Bird) between Schreier sets and the Fibonacci sequence, we introduce Schreier multisets and connect these multisets with the s-step Fibonacci sequences, defined, for each s ≥ 2, as F(s)2-s = = F(s)0 = 0, F(s)1 = 1, and F(s)n = F(s)n-1 + + F(s)n-s, for n ≥ 2. Next, we use Schreier-Type conditions on multisets to retrieve a family of sequences, which satisfy a recurrence of the form a(n) = a(n-1) + a(n-u), with a(n) = 1 for n = 1,.., u. Finally, we study nonlinear Schreier conditions and show that these conditions are related to integer decompositions, each part of which is greater than the number of parts raised to some power. © 2024 Walter de Gruyter GmbH, Berlin/Boston.eninfo:eu-repo/semantics/openAccessConference Object10.1515/9783111395593-0072-s2.0-105022175933