3 problems

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The dual-partition refinement conjecture for poset-weight partitions
Dual-partition refinement conjecture. If $|H_i|\geqslant2$ for all $i\in\Omega$ , then the dual partition of $\mathcal{Q}(\boldsymbol{H},\boldsymbol{P})$ is finer than…
Conjecturesolvedfinite-abelian-groups macwilliams-identities poset-metricsarXiv posted 2 days ago
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The Fourier-reflexivity characterization of hierarchical posets
Fourier-reflexivity characterization. If $|H_i|\geqslant2$ for all $i\in\Omega$ and $\mathcal{Q}(\boldsymbol{H},\boldsymbol{P})$ is Fourier-reflexive, then $\boldsymbol{P}$ is hier…
Conjecturesolvedfinite-abelian-groups fourier-analysis poset-metricsarXiv posted 2 days ago
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Generalized LDM criterion conjecture for poset partitioning
Generalized LDM criterion conjecture. A generalization of the LDM criterion should perform well for the poset partition problem, in the same context as LDM performs well for the cl…
Conjectureopenheuristic-algorithms partitioning-problems poset-metricsarXiv posted 2 days ago

The dual-partition refinement conjecture for poset-weight partitions