Key-avoidance for alternating sign matrices
We initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM. We enumerate alternating sign matrices whose key avoids a given set of permutation patterns in several instances. We show th...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2025-03-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | http://dmtcs.episciences.org/14058/pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM. We enumerate alternating sign matrices whose key avoids a given set of permutation patterns in several instances. We show that ASMs whose key avoids $231$ are permutations, thus any known enumeration for a set of permutation patterns including $231$ extends to ASMs. We furthermore enumerate by the Catalan numbers ASMs whose key avoids both $312$ and $321$. We also show ASMs whose key avoids $312$ are in bijection with the gapless monotone triangles of [Ayyer, Cori, Gouyou-Beauchamps 2011]. Thus key-avoidance generalizes the notion of $312$-avoidance studied there. Finally, we enumerate ASMs with a given key avoiding $312$ and $321$ using a connection to Schubert polynomials, thereby deriving an interesting Catalan identity. |
|---|---|
| ISSN: | 1365-8050 |