We first show that δ ( π ) ∈ D ( n , k ) (i.e., that it does not fall below the x -axis and that it ends at ( n , k ) ). Since π is an involution, if we ignore ...
In [SiS], Simion and Schmidt completed the study of involutions avoiding a given pattern of length three. Their results are given in Theorem 1.1 above. As done ...
Dec 19, 2002 · Abstract page for arXiv paper math/0212267: Refined Restricted Involutions.
Abstract. Define $I_n^k(\alpha)$ to be the set of involutions of $\{1,2,...,n\}$ with exactly $k$ fixed points which avoid the pattern $\alpha \in S_i$, ...
Dec 13, 2024 · Let Y be a fixed nonempty subset of X and let OT(X, Y) be the subsemigroup of OT(X) of all order-preserving transformations with ranges ...
Semantic Scholar extracted view of "Refined restricted involutions" by Emeric Deutsch et al.
Request PDF | Refined Restricted Involutions | Define Ink (α) to be the set of involutions of {1, 2, ..., n} with exactly k fixed points which avoid the ...
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Aug 23, 2021 · Recently, the study of patterns in inversion sequences was initiated by Corteel–Martinez–Savage–Weselcouch and Mansour–Shattuck ind.
Missing: involutions. | Show results with:involutions.
In a recent paper [2] the authors introduce a notion of refined restricted involutions by considering the “number of fixed points” statistic on involutions ...
Making use of a combinatorial approach, we prove two refined major-balance identities on the 321 -avoiding involutions in S n , respecting the number of ...