Stirling numbers of the first kind
E1246955
UNEXPLORED
Stirling numbers of the first kind are a family of combinatorial numbers that count permutations by their number of cycles and appear in expansions relating falling factorials to ordinary powers.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Stirling numbers of the first kind canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T16991859 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Stirling numbers of the first kind Context triple: [The Twelvefold Way, relatesTo, Stirling numbers of the first kind]
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A.
Stirling numbers of the second kind
Stirling numbers of the second kind are a family of combinatorial numbers that count the ways to partition a set of n labeled elements into k nonempty, unlabeled subsets.
-
B.
Bell numbers
Bell numbers are a sequence in combinatorics that count the number of ways to partition a finite set into nonempty, unlabeled subsets.
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C.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
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D.
Catalan numbers
Catalan numbers are a sequence of natural numbers that count a wide variety of combinatorial structures, such as correctly matched parentheses, binary tree shapes, and lattice path configurations.
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E.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Stirling numbers of the first kind Target entity description: Stirling numbers of the first kind are a family of combinatorial numbers that count permutations by their number of cycles and appear in expansions relating falling factorials to ordinary powers.
-
A.
Stirling numbers of the second kind
Stirling numbers of the second kind are a family of combinatorial numbers that count the ways to partition a set of n labeled elements into k nonempty, unlabeled subsets.
-
B.
Bell numbers
Bell numbers are a sequence in combinatorics that count the number of ways to partition a finite set into nonempty, unlabeled subsets.
-
C.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
-
D.
Catalan numbers
Catalan numbers are a sequence of natural numbers that count a wide variety of combinatorial structures, such as correctly matched parentheses, binary tree shapes, and lattice path configurations.
-
E.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.