Dyck Paths
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Generating 2-Gray codes for grand Motzkin paths and grand Dyck paths with air pockets in constant amortized time
Announce Type: cross Abstract: A grand Motzkin path with air pockets is a non-empty lattice path in the first and fourth quadrant of $\mathbb{Z}^2$, starting at the origin $(0,0)$, ending on the $x$-axis, and consisting of up-steps $(1, 1)$, horizontal steps $(1, 0)$, down-steps $(1, -k)$ where $k \geq 1$, and with no consecutive down-steps. A {grand Dyck path with air pockets} is a grand Motzkin path with air pockets that uses no horizontal steps. We present the first known 2-Gray codes for...
Discovering a Zeta Map Algorithm on Dyck Paths via Mechanistic Interpretability
Announce Type: new Abstract: Machine learning is increasingly used in mathematical discovery, but in mathematics the desired output is often not a prediction itself, but an explicit construction that can be checked independently. We study this setting through the zeta map on Dyck paths, a classical bijection in the combinatorics of the q,t-Catalan numbers. We train a deliberately small one-layer, one-head encoder-decoder transformer on this map and analyze its learned computation using...