DISCRETE CONCAVITY AND THE HALF-PLANE PROPERTY
2010 (English)In: SIAM Journal on Discrete Mathematics, ISSN 0895-4801, E-ISSN 1095-7146, Vol. 24, no 3, 921-933 p.Article in journal (Refereed) Published
Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized Puiseux series) with prescribed non-anishing properties. This family contains several of the most well studied M-concave functions in the literature. In the language of tropical geometry, we study the tropicalization of the space of polynomials with the half-plane property and show that it is strictly contained in the space of M-concave functions. We also provide a short proof of Speyer's ""hive theorem"" which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices.
Place, publisher, year, edition, pages
2010. Vol. 24, no 3, 921-933 p.
M-convex, jump system, matroid, half-plane property, tropicalization, Puiseux series, Tarski's principle, hive, Horn's conjecture
IdentifiersURN: urn:nbn:se:su:diva-48956DOI: 10.1137/090758738ISI: 000282291600014OAI: oai:DiVA.org:su-48956DiVA: diva2:376393
authorCount :12010-12-102010-12-102010-12-14Bibliographically approved