Bibliographic Details
| Title: |
Enumeration of pattern-avoiding alternating sign matrices: An asymptotic dichotomy |
| Authors: |
Bouvel, Mathilde, Egge, Eric S., Smith, Rebecca N., Striker, Jessica, Troyka, Justin M. |
| Publication Year: |
2024 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Combinatorics |
| More Details: |
We completely classify the asymptotic behavior of the number of alternating sign matrices classically avoiding a single permutation pattern, in the sense of [Johansson and Linusson 2007]. In particular, we give a uniform proof of an exponential upper bound for the number of alternating sign matrices classically avoiding one of twelve particular patterns, and a super-exponential lower bound for all other single-pattern avoidance classes. We also show that for any fixed integer $k$, there is an exponential upper bound for the number of alternating sign matrices that classically avoid any single permutation pattern and contain precisely $k$ negative ones. Finally, we prove that there must be at most $3$ negative ones in an alternating sign matrix which classically avoids both $2143$ and $3412$, and we exactly enumerate the number of them with precisely $3$ negative ones. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2411.07662 |
| Accession Number: |
edsarx.2411.07662 |
| Database: |
arXiv |
