Counting with Bounded Treewidth
summary
Claim: for Holant instances defined by symmetric signatures whose pinning profiles have at most R distinct outcomes the partition function is computable by a combinatorial dynamic program in time R^{O(t)}·poly(n) where t is treewidth and also in time R^{O(n)} on general graphs, with R the base improved from previous bounds and conjectured tight under ETH. The method uses R-regular signature classification, a binary separator decomposition recursion, and a peering oracle to enumerate equivalent pinning classes. Parity has R=2, Eulerian orientation is irregular, and the algorithm yields planar approximation consequences assuming correlation decay.
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