Introduces dualGNN, an autoregressive message-passing GNN using signed circuits to sample uniform fine regular triangulations of lattice polytopes, applied to Calabi-Yau threefolds at h^{1,1}=86 and 128.
Counting Lattice Triangulations
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abstract
We discuss the problem to count, or, more modestly, to estimate the number f(m,n) of unimodular triangulations of the planar grid of size $m\times n$. Among other tools, we employ recursions that allow one to compute the (huge) number of triangulations for small m and rather large n by dynamic programming; we show that this computation can be done in polynomial time if m is fixed, and present computational results from our implementation of this approach. We also present new upper and lower bounds for large m and n, and we report about results obtained from a computer simulation of the random walk that is generated by flips.
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hep-th 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Sampling Triangulations and Calabi-Yau Threefolds with Autoregressive GNNs
Introduces dualGNN, an autoregressive message-passing GNN using signed circuits to sample uniform fine regular triangulations of lattice polytopes, applied to Calabi-Yau threefolds at h^{1,1}=86 and 128.