3 papers
math.CO2026
The 1/3-phenomenon of placement probabilities of tilings in the semiregular hexagon
Marcus Schönfelder
We prove Krattenthaler's conjecture from 2001 about the -phenomenon for lozenge tilings of semiregular hexagons. In a first step we reduce the problem to the case of regular h…
math.CO2026
The 1/4-phenomenon of placement probabilities of tilings in the Aztec diamond
Marcus Schönfelder
We consider domino tilings of the Aztec diamond. Using the Domino Shuffling algorithm introduced by Elkies, Kuperberg, Larsen, and Propp in arXiv:math/9201305, we are able to gener…
math.CO2026
More minor summation formulae
Shane Chern, Theresia Eisenkölbl, Ilse Fischer +8
We prove determinantal-Pfaffian formulae that simultaneously generalise the Pfaffian minor summation formula of Ishikawa and Wakayama and Byun's recent minor summation formula. The…