The Squish Map and the SL_2 Double Dimer Model
| dc.contributor.advisor | Young, Benjamin | |
| dc.contributor.author | Foster, Leigh | |
| dc.date.accessioned | 2024-08-07T21:29:02Z | |
| dc.date.available | 2024-08-07T21:29:02Z | |
| dc.date.issued | 2024-08-07 | |
| dc.description.abstract | A plane partition, whose 3D Young diagram is made of unit cubes, can be approximated by a “coarser” plane partition, made of cubes of side length 2. Indeed, there are two such approximations obtained by “rounding up” or “rounding down” to the nearest cube. We relate this coarsening (or downsampling) operation to the squish map introduced by the second author in earlier work. We exhibit a related measure-preserving map between the dimer model on the honeycomb graph, and the SL_2 double dimer model on a coarser honeycomb graph; we compute the most interesting special case of this map, related to plane partition q-enumeration with 2-periodic weights. As an application, we specialize the weights to be certain roots of unity, obtain novel generating functions (some known, some new, and some conjectural) that (−1)-enumerate certain classes of pairs of plane partitions according to how their dimer configurations interact. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/29736 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | combinatorics | en_US |
| dc.subject | linear algebra | en_US |
| dc.subject | statistical mechanics | en_US |
| dc.title | The Squish Map and the SL_2 Double Dimer Model | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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