---
res:
  bibo_abstract:
  - "We consider local dynamics of the dimer model (perfect matchings) on hypercubic
    boxes [n] \r\nd . These consist of successively switching the dimers along alternating
    cycles of prescribed (small) lengths. We study the connectivity properties of
    the dimer configuration space equipped with these transitions. Answering a question
    of Freire, Klivans, Milet, and Saldanha, we show that in three dimensions any
    configuration admits an alternating cycle of length at most 6. We further establish
    that any configuration on [n] d  features order n d−2  alternating cycles of length
    at most 4d−2. We also prove that the dynamics of dimer configurations on the unit
    hypercube of dimension d is ergodic when switching alternating cycles of length
    at most 4d−4. Finally, in the planar but non-bipartite case, we show that parallelogram-shaped
    boxes in the triangular lattice are ergodic for switching alternating cycles of
    lengths 4 and 6 only, thus improving a result of Kenyon and Rémila, which also
    uses 8-cycles. None of our proofs make reference to height functions.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Ivailo
      foaf_name: Hartarsky, Ivailo
      foaf_surname: Hartarsky
  - foaf_Person:
      foaf_givenName: Lyuben
      foaf_name: Lichev, Lyuben
      foaf_surname: Lichev
      foaf_workInfoHomepage: http://www.librecat.org/personId=9aa8388e-d003-11ee-8458-c4c1d7447977
  - foaf_Person:
      foaf_givenName: Fabio Lucio
      foaf_name: Toninelli, Fabio Lucio
      foaf_surname: Toninelli
  bibo_doi: 10.4171/aihpd/200
  dct_date: 2024^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2308-5827
  - http://id.crossref.org/issn/2308-5835
  dct_language: eng
  dct_publisher: EMS Press@
  dct_title: Local dimer dynamics in higher dimensions@
...