5.237. longest_increasing_sequence
DESCRIPTION | LINKS | AUTOMATON |
- Origin
constraint on sequences
- Constraint
- Synonym
.
- Arguments
- Restrictions
- Purpose
is the largest difference between the first and the last value of the maximum increasing sequences of the collection .
A sequence of consecutive variables () of the collection of variables is a maximum increasing sequence if all the following conditions simultaneously apply:
,
or ,
or .
- Example
-
FigureΒ 5.237.1 gives a graphical representation of the first example of the Example slot with its two maximum increasing sequences in red of respective size 0 and 7. The corresponding constraint holds since its first argument is fixed to the maximum size 7.
Figure 5.237.1. Illustration of the first example of the Example slot: a sequence of eight variables , , , , , , , respectively fixed to values 10, 8, 8, 6, 4, 9, 11, 8 and its two maximum increasing sequences in red of respective size and .
- Typical
- Symmetry
One and the same constant can be added to the attribute of all items of .
- Arg. properties
Functional dependency: determined by .
- 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 18 122 750 4412 25382 144314 2 1 16 161 1398 11361 89132 685090 3 - 10 162 1942 20816 211106 2074365 4 - - 110 2024 28930 375084 4603682 5 - - - 1410 30134 506766 7792840 6 - - - - 21072 522648 10197174 7 - - - - - 363602 10379696 8 - - - - - - 7156690 Solution count for : domains
- See also
common keyword: , Β (sequence).
- Keywords
characteristic of a constraint: automaton, automaton with counters, automaton with same input symbol.
combinatorial object: sequence.
constraint arguments: reverse of a constraint, pure functional dependency.
- Automaton
FigureΒ 5.237.2 depicts the automaton associated with the constraint.
Figure 5.237.2. Automaton of the constraint and its glue matrix (note that the reverse of the constraint is the constraint)
Figure 5.237.3. Hypergraph of the reformulation corresponding to the automaton of the constraint