Homogeneous character induction

The homogeneous weight partition and its character-theoretic dual

The values of the normalized homogeneous weight are determined for arbitrary finite Frobenius rings and expressed in a form that is independent from a generating character and the Möbius function on the ring. The weight naturally induces a partition of the ring, which is invariant under left or right multiplication by units. It is shown that the character-theoretic left-sided dual of this parti...

ON THE CHARACTER AND r-WEIGHT OF HOMOGENEOUS COMPACTA

Under GCH, k(X) _< ~(X) for every homogeneous compactum X. CH implies that a homogeneous compactum of countable ~r-weight is first countable. There is a compact space of countable 7r-weight and uncountable character which is homogeneous under MA+-~CH, but not under CH.

Induction, bounding, weak combinatorial principles, and the homogeneous model theorem

Goncharov and Peretyat’kin independently gave necessary and sufficient conditions for when a set of types of a complete theory T is the type spectrum of some homogeneous model of T . Their result can be stated as a principle of second order arithmetic, which we call the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previou...

Homogeneous Catalysis Homogeneous Catalysis

Homogeneous and Non Homogeneous Algorithms

Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non-homogeneous algorithms.1 Although both classes contain algorithms with worst and best cases, homogeneous algorithms behave uniformly on all instances. This partition clarifies in a completely mathematical way the previously ment...