Global structure of integer partitions sequences

Physics – Computational Physics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

25 pages, submitted to The Electronic Journal of Combinatorics

Scientific paper

Integer partitions are deeply related to many phenomena in statistical physics. A question naturally arises which is of interest to physics both on "purely" theoretical and on practical, computational grounds. Is it possible to apprehend the global pattern underlying integer partition sequences and to express the global pattern compactly, in the form of a "matrix" giving all of the partitions of N into exactly M parts? This paper demonstrates that the global structure of integer partitions sequences (IPS) is that of a complex tree. By analyzing the structure of this tree, we derive a closed form expression for a map from (N, M) to the set of all partitions of a positive integer N into exactly M positive integer summands without regard to order. The derivation is based on the use of modular arithmetic to solve an isomorphic combinatoric problem, that of describing the global organization of the sequence of all ordered placements of N indistinguishable balls into M distinguishable non-empty bins or boxes. This work has the potential to facilitate computations of important physics and to offer new insights into number theoretic problems.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Global structure of integer partitions sequences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Global structure of integer partitions sequences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global structure of integer partitions sequences will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-662242

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.