Proof of Blum's conjecture on hexagonal dungeons

Mihai Ciucu, Tri Lai

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Matt Blum conjectured that the number of tilings of the hexagonal dungeon of sides a, 2. a, b, a, 2a, b (where b ≥ 2a) is 132a214⌊a2/2⌋ (Propp, 1999 [4]). In this paper we present a proof for this conjecture using Kuo's Graphical Condensation Theorem (Kuo, 2004 [2]).

Original languageEnglish (US)
Pages (from-to)273-305
Number of pages33
JournalJournal of Combinatorial Theory. Series A
Issue number1
StatePublished - Jul 2014
Externally publishedYes


  • Aztec dungeons
  • Dual graph
  • Graphical condensation
  • Hexagonal dungeons
  • Perfect matchings
  • Tilings


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