1 citations · 2 across the 11 of their papers we have counts for
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New Planar Algorithms and a Full Complexity Classification of the Eight-Vertex Model
Austen Fan, Jin-Yi Cai, Shuai Shao +1
We prove a complete complexity classification theorem for the planar eight-vertex model. For every parameter setting in for the eight-vertex model, the partition func…
Restricted Holant Dichotomy on Domains 3 and 4
Yin Liu, Austen Z. Fan, Jin-Yi Cai
denotes a class of counting problems specified by a constraint function . We prove complexity dichotomy theorems for in…
Planar 3-way Edge Perfect Matching Leads to A Holant Dichotomy
Jin-Yi Cai, Austen Z. Fan
We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint func…
Bipartite 3-Regular Counting Problems with Mixed Signs
Jin-Yi Cai, Austen Z. Fan, Yin Liu
We prove a complexity dichotomy for a class of counting problems expressible as bipartite 3-regular Holant problems. For every problem of the form $\operatorname{Holant}\left(f\mid…
Dichotomy Result on 3-Regular Bipartite Non-negative Functions
Austen Z. Fan, Jin-Yi Cai
We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function $f = [x_…