Distinct matroid base weights and additive theory. (English) Zbl 1259.11095
Chudnovsky, David (ed.) et al., Additive number theory. Festschrift in honor of the sixtieth birthday of Melvyn B. Nathanson. New York, NY: Springer (ISBN 978-0-387-37029-3/hbk; 978-0-387-68361-4/ebook). 145-151 (2010).
Let \(M\) be a matroid on a a set \(E\) and let \(w: E \to G\) be a weight function, where \(G\) is a cyclic group. Assuming that \(w(E)\) satisfies the Pollard’s condition, the authors obtain a formula for the number of distinct base weights. If \(|G|\) is prime, the result coincides with a result of Schrijver and Seymour.
The authors also describe equality cases in their formula. In the prime case, their result generalizes Vosper’s Theorem.
For the entire collection see [Zbl 1196.11005].
The authors also describe equality cases in their formula. In the prime case, their result generalizes Vosper’s Theorem.
For the entire collection see [Zbl 1196.11005].
Reviewer: Kelly J. Pearson (Murray)
MSC:
| 11P70 | Inverse problems of additive number theory, including sumsets |
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
