Triple

T1249043
Position Surface form Disambiguated ID Type / Status
Subject multinomial theorem E26831 entity
Predicate connectedTo P37 FINISHED
Object stars and bars method
The stars and bars method is a classic combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinct bins, often applied to problems involving nonnegative integer solutions to equations.
E141902 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: stars and bars method | Statement: [multinomial theorem, connectedTo, stars and bars method]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: stars and bars method
Context triple: [multinomial theorem, connectedTo, stars and bars method]
  • A. Pascal's identity
    Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
  • B. binomial theorem
    The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
  • C. multinomial theorem
    The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
  • D. Pascal's triangle
    Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
  • E. Bernoulli trials
    Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: stars and bars method
Triple: [multinomial theorem, connectedTo, stars and bars method]
Generated description
The stars and bars method is a classic combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinct bins, often applied to problems involving nonnegative integer solutions to equations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: stars and bars method
Target entity description: The stars and bars method is a classic combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinct bins, often applied to problems involving nonnegative integer solutions to equations.
  • A. Pascal's identity
    Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
  • B. binomial theorem
    The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
  • C. multinomial theorem
    The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
  • D. Pascal's triangle
    Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
  • E. Bernoulli trials
    Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69a49487a9c48190ba9b05348fd1b53f completed March 1, 2026, 7:33 p.m.
NER Named-entity recognition batch_69a4bf83b32c81908648e5748b897247 completed March 1, 2026, 10:36 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac8f7f59148190a9f1cbd4af8a115e completed March 7, 2026, 8:50 p.m.
NEDg Description generation batch_69ac8ff7ae0c81908ca8ace1f4159383 completed March 7, 2026, 8:52 p.m.
NED2 Entity disambiguation (via description) batch_69ac905e121c819093c9d960b53a45b7 completed March 7, 2026, 8:53 p.m.
Created at: March 1, 2026, 7:47 p.m.