TY - JOUR

T1 - Resonance sequences and focal decomposition

AU - Alvarez, S.

AU - Berend, D.

AU - Birbrair, L.

AU - Girão, D.

N1 - Funding Information:
∗ D. Girão was supported by CAPES/FULBRIGHT grant BEX 2411059. Received March 15, 2007 and in revised form July 25, 2007

PY - 2009/3/1

Y1 - 2009/3/1

N2 - Let α = {α1, ...,αk} be a finite multiset of non-negative real numbers. Consider the sequence of all positive integer multiples of all α i 's, and note the multiplicity of each term in this sequence. This sequence of multiplicities is the resonance sequence generated by {α 1, ...,αk}. Two multisets are combinatiorially equivalent if they generate the same resonance sequence. The paper is devoted to the classification of multisets up to combinatorial equivalence. We show that the problem of combinatorial equivalence of multisets is closely related to the problem of classification of systems of second order ordinary differential equations up to focal equivalence.

AB - Let α = {α1, ...,αk} be a finite multiset of non-negative real numbers. Consider the sequence of all positive integer multiples of all α i 's, and note the multiplicity of each term in this sequence. This sequence of multiplicities is the resonance sequence generated by {α 1, ...,αk}. Two multisets are combinatiorially equivalent if they generate the same resonance sequence. The paper is devoted to the classification of multisets up to combinatorial equivalence. We show that the problem of combinatorial equivalence of multisets is closely related to the problem of classification of systems of second order ordinary differential equations up to focal equivalence.

UR - http://www.scopus.com/inward/record.url?scp=65549169969&partnerID=8YFLogxK

U2 - 10.1007/s11856-009-0029-6

DO - 10.1007/s11856-009-0029-6

M3 - Article

AN - SCOPUS:65549169969

VL - 170

SP - 269

EP - 284

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -