10 citations · 13 across the 14 of their papers we have counts for
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On the six-vertex model's free energy
Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun +2
In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary…
Rotational invariance in critical planar lattice models
Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun +2
We prove that the large-scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the squ…
On the size of for algebraic
Dmitry Krachun, Fedor Petrov
For a finite set and real , let . Combining a structural theorem of Freiman on sets with small doubling constants together wit…
On sums of four pentagonal numbers with coefficients
Dmitry Krachun, Zhi-Wei Sun
The pentagonal numbers are the integers given by . Let be one of the triples and . We show that eac…
Each positive rational number has the form
Dmitry Krachun, Zhi-Wei Sun
In this note, we show that each positive rational number can be written as , where is Euler's totient function and and are positive integers.