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
SN - 0021-2172
VL - 170
SP - 269
EP - 284
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -