Correct predictions are in blue. If we detect only a subset of a labelled sentence, we highlight the caught part as blue, the missing part light blue. False positives are in green and false negatives are in red.

Problem 044 (Steiner triple systems) — Constraint detection

The ternary Steiner problem of order n consists of finding a set of $ n. -LRB- n-1 -RRB- / 6 $ triples of distinct integer elements in $ \ -LCB- 1 , \ dots , n \ -RCB- $ such that any two triples have at most one common element . It is a hypergraph problem coming from combinatorial mathematics where n modulo 6 has to be equal to 1 or 3 . One possible solution for $ n = 7 $ is -LCB- -LCB- 1 , 2 , 3 -RCB- , -LCB- 1 , 4 , 5 -RCB- , -LCB- 1 , 6 , 7 -RCB- , -LCB- 2 , 4 , 6 -RCB- , -LCB- 2 , 5 , 7 -RCB- , -LCB- 3 , 4 , 7 -RCB- , -LCB- 3 , 5 , 6 -RCB- -RCB- . The solution contains $ 7 * -LRB- 7-1 -RRB- / 6 = 7 $ triples . This is a particular case of the more general Steiner system . More generally still , you may refer to Balanced Incomplete Block Designs -LRB- BIBD : prob028 -RRB- . In fact , a Steiner Triple System with n elements is a BIBD$ -LRB- n , n. -LRB- n-1 -RRB- / 6 , -LRB- n-1 -RRB- / 2 , 3 , 1 -RRB- $

Problem 044 (Steiner triple systems) — Detection of the decisions and objects to be modeled

The ternary Steiner problem of order n consists of finding a set of $ n. -LRB- n-1 -RRB- / 6 $ triples of distinct integer elements in $ \ -LCB- 1 , \ dots , n \ -RCB- $ such that any two triples have at most one common element . It is a hypergraph problem coming from combinatorial mathematics where n modulo 6 has to be equal to 1 or 3 . One possible solution for $ n = 7 $ is -LCB- -LCB- 1 , 2 , 3 -RCB- , -LCB- 1 , 4 , 5 -RCB- , -LCB- 1 , 6 , 7 -RCB- , -LCB- 2 , 4 , 6 -RCB- , -LCB- 2 , 5 , 7 -RCB- , -LCB- 3 , 4 , 7 -RCB- , -LCB- 3 , 5 , 6 -RCB- -RCB- . The solution contains $ 7 * -LRB- 7-1 -RRB- / 6 = 7 $ triples . This is a particular case of the more general Steiner system . More generally still , you may refer to Balanced Incomplete Block Designs -LRB- BIBD : prob028 -RRB- . In fact , a Steiner Triple System with n elements is a BIBD$ -LRB- n , n. -LRB- n-1 -RRB- / 6 , -LRB- n-1 -RRB- / 2 , 3 , 1 -RRB- $

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