Gordon–McMahon conjecture on Tutte polynomials of series-parallel posets

Let $\mathrm{SP}$ be the class of series-parallel posets, and let $T(P;x,y)$ denote the Tutte polynomial of the greedoid induced by a poset $P$ . The Gordon–McMahon conjecture asserts that, for all $P,Q\in\mathrm{SP}$ , $T(P;x,y)=T(Q;x,y)$ if and only if $P\cong Q$ .

References

Primary source

arXiv

Additional references

On the Tutte polynomial of series-parallel posets — arXiv — Jianxuan Luo, Tingzeng Wu, Hong-Jian Lai

Posted 1 week ago · edited 1 week ago

Progress summary

Refreshed 1 week ago

Claimed progress

A new paper proves the conjectured equivalence for a broader class of series-parallel posets, but the full conjecture remains open.

The Gordon–McMahon conjecture concerns a reconstruction equivalence for series-parallel posets. The latest advance is by Jianxuan Luo, Tingzeng Wu, and Hong-Jian Lai.

September 2026 enlargement of the positive class

Luo, Wu, and Lai report that the known positive class can be enlarged to a class $H$ , establishing the conjectured equivalence whenever one of the two posets lies in $H$ . This is claimed progress rather than a resolution: the case of arbitrary pairs remains open, and the result has not been independently verified here.

Current status (as of September 2026): The conjecture is proved only for the enlarged class $H$ when one poset lies in $H$ ; the general case remains open.

Sources

No solutions have been posted yet.