5.252. min_decreasing_slope
DESCRIPTION | LINKS | AUTOMATON |
- Origin
Motivated by time series.
- Constraint
- Arguments
- Restrictions
- Purpose
Given a sequence of variables , sets to 0 if , otherwise sets to .
- Example
-
The first constraint holds since the sequence contains two decreasing subsequences and and the minimum slope is equal to as shown on FigureΒ 5.252.1.
Figure 5.252.1. Illustration of the first example of the Example slot: a sequence of nine variables , , , , , , , , respectively fixed to values 1, 1, 5, 8, 6, 2, 4, 1, 5 and the corresponding minimum slope on the strictly decreasing subsequences and ()
- Typical
- Symmetry
One and the same constant can be added to the attribute of all items of .
- Arg. properties
Functional dependency: determined by .
- Usage
Getting the minimum slope over the decreasing sequences of time series.
- Counting
-
Length () 2 3 4 5 6 7 8 Solutions 9 64 625 7776 117649 2097152 43046721 Number of solutions for : domains
Length () 2 3 4 5 6 7 8 Total 9 64 625 7776 117649 2097152 43046721 Parameter value 0 6 20 70 252 924 3432 12870 1 2 22 256 3512 56537 1051936 22280084 2 1 14 145 1864 28728 515372 10601773 3 - 8 98 1062 14729 255076 5106480 4 - - 56 704 8853 133672 2475484 5 - - - 382 5266 78198 1369232 6 - - - - 2612 41330 730161 7 - - - - - 18136 341618 8 - - - - - - 129019 Solution count for : domains
- Keywords
characteristic of a constraint: automaton, automaton with counters.
combinatorial object: sequence.
constraint arguments: reverse of a constraint, pure functional dependency.
- Cond. implications
- Automaton
FigureΒ 5.252.2 depicts the automaton associated with the constraint. To each pair of consecutive variables of the collection corresponds a signature variable . The following signature constraint links , and : .
Figure 5.252.2. Automaton for the constraint and its glue matrix (note that the reverse of is )