adding the motzkin paper

Author: christianbean

_authors/bernini.md

@@ -0,0 +1,10 @@
+---
+status: collaborator
+short_name: bernini
+first_name: Antonio
+name: Antonio Bernini
+position: 
+---
+Antonio is ...
+
+<!-- - [MathSciNet Profile]() -->

_authors/cervetti.md

@@ -0,0 +1,9 @@
+status: collaborator
+short_name: cervetti
+first_name: Matteo
+name: Matteo Cervetti
+position: 
+---
+Matteo is ...
+
+<!-- - [MathSciNet Profile]() -->

_authors/ferrari.md

@@ -0,0 +1,9 @@
+status: collaborator
+short_name: ferrari
+first_name: Luca
+name: Luca Ferrari
+position: 
+---
+Luca is ...
+
+<!-- - [MathSciNet Profile]() -->

_papers/2021-08-06-motzkin.md

@@ -0,0 +1,20 @@
+title: Pattern avoiding Motzkin paths are almost rational
+
+journal: Submitted
+
+authors:
+- bean
+- bernini
+- cervetti
+- ferrari
+
+projects:
+---
+![Motzkin paths avoiding HH]({{site.baseurl}}/assets/img/motzkin.png){:align="right" height="200px"}
+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). Moreover, an algorithm is provided for finding the generating function, also in the more general case of an arbitrary set of patterns. In addition, such an algorithm allows us to find a combinatorial specification for pattern avoiding Motzkin paths, which can be used not only for enumeration, but also for exhaustive and random generation.
+<!-- The paragraph above is an adaptation of the abstract. 2021-08-06-->
+
+## Download the paper
+- [arXiv](https://arxiv.org/abs/2108.03037)
+
+## Presentations