Smith normal form in combinatorics
Copyright policy )Smith normal form in combinatorics
This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith normal form of random integer matrices. We then give some examples of Smith normal form and diagonal form arising from (1) symmetric functions, (2) a result of Carlitz, Roselle, and Scoville, and (3) the Varchenko matrix of a hyperplane arrangement.
17 pages, 3 figures
- Miami University United States
- Massachusetts Institute of Technology United States
- University System of Ohio United States
diagonal form, Canonical forms, reductions, classification, Exact enumeration problems, generating functions, Sequences and sets, random matrix, Smith normal form, Jacobi-Trudi matrix, 05E99, 15A21, critical group, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Varchenko matrix
diagonal form, Canonical forms, reductions, classification, Exact enumeration problems, generating functions, Sequences and sets, random matrix, Smith normal form, Jacobi-Trudi matrix, 05E99, 15A21, critical group, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Varchenko matrix
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).48 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!