Name
Abstract | ||
|---|---|---|
We examine classes of real-valued functions of 0-1 variables closed under algebraic operations as well as topological convergence, and having a certain local characteristic (requiring that any function not in the class should have a k-variable minor not belonging to this class). It is shown that for k=2, the only 4 maximal classes with these properties are those of submodular, supermodular, monotone increasing and monotone decreasing functions. All the 13 locally defined closed classes are determined and shown to be intersections of the 4 maximal ones. All maximal classes for k=3 are determined and characterized by the sign of higher order derivatives of the functions in the class. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.dam.2009.02.005 | Discrete Applied Mathematics |
Keywords | Field | DocType |
topological convergence,pseudo-boolean functions,certain local characteristic,algebraic operation,closed class,topological closure condition,pseudo-boolean function,real-valued function,maximal class,higher order derivative,higher order,value function | Boolean function,Discrete mathematics,Topology,Monotonic function,Combinatorics,Algebraic number,Characteristic function (probability theory),Submodular set function,Real-valued function,Monotone polygon,Mathematics,Algebraic operation | Journal |
Volume | Issue | ISSN |
157 | 13 | Discrete Applied Mathematics |
Citations | PageRank | References |
0 | 0.34 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stephan Foldes | 1 | 175 | 19.36 |
| Peter L. Hammer | 2 | 1996 | 288.93 |