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On the generating functions of pattern-avoiding Motzkin paths

Autor: Bean, Christian, Bernini, Antonio, Cervetti, Matteo, Ferrari, Luca

Using a recursive approach, we show that the generating function for sets of Motzkin paths avoiding a single (not necessarily consecutive) pattern is rational over $x$ and the Catalan generating function $C(x) = \frac{1-\sqrt{1-4x^2}}{2x^2}$, where $

Externí odkaz: http://arxiv.org/abs/2108.03037

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A generating tree with a single label for permutations avoiding the vincular pattern 1-32-4

Autor: Cervetti, Matteo

In this paper we continue the study of permutations avoiding the vincular pattern $1-32-4$ by constructing a generating tree with a single label for these permutations. This construction finally provides a clearer explanation of why a certain recursi

Externí odkaz: http://arxiv.org/abs/2103.00246

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Pattern avoidance in the matching pattern poset

Autor: Cervetti, Matteo, Ferrari, Luca

A matching of the set $[2n]=\{ 1,2,\ldots ,2n\}$ is a partition of $[2n]$ into blocks with two elements, i.e. a graph on $[2n]$ such that every vertex has degree one. Given two matchings $\sigma$ and $\tau$ , we say that $\sigma$ is a pattern of $\ta

Externí odkaz: http://arxiv.org/abs/2009.01024

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Enumerative combinatorics of intervals in the Dyck pattern poset

Autor: Bernini, Antonio, Cervetti, Matteo, Ferrari, Luca, Steingrimsson, Einar

We initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations. In m

Externí odkaz: http://arxiv.org/abs/1910.00299

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