Matroid theory and Chern–Simons

Matroid theory

The comments below apply to all printings of the book dated 2005 or earlier. The table following contains more than just a list of typing errors. Some statements and proofs have been corrected, simplified, or clarified. Moreover, the current status has been given for all the unsolved problems or conjectures that appear in Chapter 14. For those changes that simply involve the insertion of extra ...

Matroid Theory and Supergravity

In this work, we consider matroid theory. After presenting three different (but equivalent) definitions of matroids, we mention some of the most important theorems of such theory. In particular, we note that every matroid has a dual matroid and that a matroid is regular if and only if it is binary and includes no Fano matroid or its dual. We show a connection between this last theorem and octon...

Distinct Matroid Base Weights and Additive Theory

Let M be a matroid on a set E and let w : E −→ G be a weight function, where G is a cyclic group. Assuming that w(E) satisfies the Pollard’s Condition (i.e. Every non-zero element of w(E)−w(E) generates G), we obtain a formulae for the number of distinct base weights. If |G| is a prime, our result coincides with a result Schrijver and Seymour. We also describe Equality cases in this formulae. I...

Locally Repairable Codes and Matroid Theory

of the bachelor's thesis Abstract: Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this tends to yield codes for which error correction requires an unrealistic amount of communication between storage nodes. LRCs s...

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