Partitions of Minimal Length on Manifolds

Minimal r-Complete Partitions

A minimal r-complete partition of an integer m is a partition of m with as few parts as possible, such that all the numbers 1, . . . , rm can be written as a sum of parts taken from the partition, each part being used at most r times. This is a generalization of M-partitions (minimal 1-complete partitions). The number of M-partitions of m was recently connected to the binary partition function ...

A note on limit shapes of minimal difference partitions

We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. This paper is dedicated to Professor Leonid Pastur for his 70th anniversary. A partition of a natural integer E [1] is a decomposition of E as a sum of a nonincreasing sequence of positive integers {hj}, i.e., E = ∑ j hj such that hj ≥ hj+1, for j = 1, 2 . . .....

On the Minimal Length of Semigroup Presentations

We define the length of a semigroup presentation and related ideas. Theoretical results and bounds are presented, gained while investigating the lengths of groups defined by semigroup presentations. Minimal length semigroup presentations are obtained in certain cases. AMS Mathematics Subject Classification (2000): 20F05, 20M05

On Minimal Length Factorizations of Finite Groups

Minimal Triangulations of 3 - manifolds