Problems
No person has reviewed any of this; every judgement here is a machine's.
Must every r-differential poset have at least as many elements in each rank as Y^r, the r-th Cartesian power of Young's lattice? For r = 3 the new construction has fourth-rank size 50 against 51 for Y^3.
On the basis of experiments up to 5000 nodes, Papamanthou and Tollis conjectured a relation between the longest paths produced by their MaxSTN and MinSTN algorithms for st-orientations of biconnected graphs. A counterexample refutes it.
If a smooth bounded domain in R^n admits a Neumann eigenfunction of the Laplacian that is constant on the boundary, must the domain be a ball? Pompeiu posed an equivalent integral-equation form in 1929; Schiffer's 1957 reformulation via…
The paper gives counterexamples in dimensions eight and nine to two problems: the Cartesian-product problem posed by Cassels for critical determinants and formulated by Zong for lattice packings, and a question raised by Sarnak, formulated…