@article{347f6692f6ce46b28e545dafde9daf23,
title = "Counting independent sets in regular hypergraphs",
abstract = "Amongst d-regular r-uniform hypergraphs on n vertices, which ones have the largest number of independent sets? While the analogous problem for graphs (originally raised by Granville) is now well-understood, it is not even clear what the correct general conjecture ought to be; our goal here is to propose such a generalisation. Lending credence to our conjecture, we verify it within the class of {\textquoteleft}quasi-bipartite{\textquoteright} hypergraphs (a generalisation of bipartite graphs that seems natural in this context) by adopting the entropic approach of Kahn.",
keywords = "Entropy, Hypergraphs, Independent sets",
author = "J{\'o}zsef Balogh and B{\'e}la Bollob{\'a}s and Bhargav Narayanan",
note = "Funding Information: The first author was partially supported by NSF grant DMS-1764123 , an Arnold O. Beckman Research Award (UIUC Campus Research Board 18132) and the Langan Scholar Fund (UIUC), the second author was supported by NSF grant DMS-1855745 , and the third author wishes to acknowledge support from NSF grant DMS-1800521 . Funding Information: The first author was partially supported by NSF grant DMS-1764123, an Arnold O. Beckman Research Award (UIUC Campus Research Board 18132) and the Langan Scholar Fund (UIUC), the second author was supported by NSF grant DMS-1855745, and the third author wishes to acknowledge support from NSF grant DMS-1800521. Part of this work was done while the first author was a visiting fellow commoner at Trinity College, Cambridge; we thank Trinity College for their hospitality. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = may,
doi = "10.1016/j.jcta.2021.105405",
language = "English (US)",
volume = "180",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
}