Suborbits in Knaster's problem

Knaster's Problem for (Z2)k-Symmetric Subsets of the Sphere S2k-1

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In this paper some new cases of Knaster's problem on continuous maps from spheres are established. In particular, we consider an almost orbit of a p-torus X on the sphere, a continuous map f from the sphere to the real line or real plane, and show that X can be rotated so that f becomes constant on X.

Suborbits in Infinite Primitive Permutation Groups

For every infinite cardinal κ, we construct a primitive permutation group which has a finite suborbit paired with a suborbit of size κ. This answers a question of Peter M. Neumann.

An Equilibrium Analysis of Knaster's Fair Division Procedure

In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to effi ciently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding strategies. We find that, expost, the equilibrium allocation is still effi cient,...

On the Point Stabilizers of Transitive Groups with Non-self-paired Suborbits of Length

In [7] a characterization of transitive permutation groups having a non-self-paired suborbit of length 2 (with respect to which the corresponding orbital graph is connected) was obtained in terms of their point stabilizers. As a consequence, elementary abelian groups were proved to be the only possible abelian point stabilizers arising from such actions, and D8 was shown to be the only nonabeli...