BdGN's largest-entry conjecture for the open B model

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At q=e2iπ/3q=e^{2i\pi/3} and in the homogeneous limit, let

be the ground-state eigenvector of the open-boundary Hamiltonian for the $B_r$ model, normalized so that its smallest entry is $1$. Let $A_V(r)$ denote the corresponding Vertically Symmetric Alternating Sign Matrix enumeration (with the even case identified with the relevant Cyclically Symmetric Transpose Complement Plane Partition enumeration). **BdGN's largest-entry conjecture.** The largest entry of

, with arches connecting consecutive points, is AV(r)A_V(r). The sum-of-entries formula is established in the supplied discussion, whereas this largest-entry formula is presented as an unproved assertion.

References

Primary source

P. Di Francesco and P. Zinn-Justin, “From Orbital Varieties to Alternating Sign Matrices”, arXiv:math-ph/0512047 (2005).

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