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Pfaffian

Relationships observed in Wikidata. Connections do not establish verification or source support.

Release: sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

Provider: Wikidata · graph projection only.

OBSERVED · GRAPH-PROJECTION · NOT ADMITTED · NOT VERIFIED · NOT SUPPORT

Edge identity is the provider property id (for example P31). It is not a Counterpedia predicate.

Development requests are not available on this deployment. The observed entity and its graph links remain readable.

Relationships of Pfaffian

Show relationship types (drawing only; the text lists are unaffected)
Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)named after (Observed provider relationships)instance of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)different from (Observed provider relationships)Relationship label not yet available (Observed provider relationships)subclass of (Observed provider relationships)notable work (Observed provider relationships)Pfaffian — Wikidata entity (Q1189744)PfaffianWIKIDATA ENTITYWikiProject Mathematics — Wikidata entity (Q8487137)WikiProjectMathematicsWIKIDATA ENTITYArthur Cayley — Wikidata entity (Q159430)Arthur CayleyWIKIDATA ENTITYJohann Friedrich Pfaff — Wikidata entity (Q77361)Johann FriedrichPfaffWIKIDATA ENTITYmathematical concept — Wikidata entity (Q24034552)mathematicalconceptWIKIDATA ENTITY1852 — Literal value (wikidata:literal:4:1852)1852LITERAL VALUEPfaffian function — Wikidata entity (Q7179766)PfaffianfunctionWIKIDATA ENTITY\operatorname{pf}(A)=\frac1{2^nn!} \sum_{\sigma \in S_{2n}}\operatorname{sgn}(\sigma) \prod _{i=1}^n A_{\sigma (2i-1),\sigma (2i)} — Literal value (wikidata:literal:6:\operatorname{pf}(A)=\frac1{2^nn!} \sum_{\sigma \in S_{2n}}\operatorname{sgn}(\sigma) \prod _{i=1}^n A_{\sigma (2i-1),\sigma (2i)})\operatorname{pf}(A)=\frac1{2^n…LITERAL VALUEdeterminant — Wikidata entity (Q178546)determinantWIKIDATA ENTITY

Legend

  • Governed record relationships (solid)
  • Countergraph traversal (dashed)
  • Countergraph evidence (dotted)
  • Observed provider relationships (dash-dot)
  • Structurally derived (sparse dots)

Node shape identifies node kind only. Size, color, and position carry no meaning beyond hop distance from the root.

A line means a supported artifact carried an explicit structured relation. It does not mean the relation is true, admitted, verified, or authoritative.

Graph as text

Nodes (9)

  • Pfaffian — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q1189744
    stable_ref
    Q1189744
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q1189744
    provider
    wikidata
    entity_href
    /entries/wikidata/Q1189744
  • WikiProject Mathematics — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q8487137
    stable_ref
    Q8487137
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q8487137
    provider
    wikidata
    entity_href
    /entries/wikidata/Q8487137
  • Arthur Cayley — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q159430
    stable_ref
    Q159430
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q159430
    provider
    wikidata
    entity_href
    /entries/wikidata/Q159430
  • Johann Friedrich Pfaff — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q77361
    stable_ref
    Q77361
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q77361
    provider
    wikidata
    entity_href
    /entries/wikidata/Q77361
  • mathematical concept — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q24034552
    stable_ref
    Q24034552
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q24034552
    provider
    wikidata
    entity_href
    /entries/wikidata/Q24034552
  • 1852 — Literal value
    Technical details
    node_id
    wikidata:literal:4:1852
    stable_ref
    wikidata:literal:4:1852
    node_kind
    wikidata_literal
    plane
    provider_observed
  • Pfaffian function — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q7179766
    stable_ref
    Q7179766
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q7179766
    provider
    wikidata
    entity_href
    /entries/wikidata/Q7179766
  • \operatorname{pf}(A)=\frac1{2^nn!} \sum_{\sigma \in S_{2n}}\operatorname{sgn}(\sigma) \prod _{i=1}^n A_{\sigma (2i-1),\sigma (2i)} — Literal value
    Technical details
    node_id
    wikidata:literal:6:\operatorname{pf}(A)=\frac1{2^nn!} \sum_{\sigma \in S_{2n}}\operatorname{sgn}(\sigma) \prod _{i=1}^n A_{\sigma (2i-1),\sigma (2i)}
    stable_ref
    wikidata:literal:6:\operatorname{pf}(A)=\frac1{2^nn!} \sum_{\sigma \in S_{2n}}\operatorname{sgn}(\sigma) \prod _{i=1}^n A_{\sigma (2i-1),\sigma (2i)}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • determinant — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q178546
    stable_ref
    Q178546
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q178546
    provider
    wikidata
    entity_href
    /entries/wikidata/Q178546

Edges (9)

  • Pfaffian — Relationship label not yet available → WikiProject Mathematics — Observed provider relationships
    Technical details
    machine_predicate
    P6104
    predicate_ref
    wikidata:property:P6104
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:0:P6104
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Pfaffian — Relationship label not yet available → Arthur Cayley — Observed provider relationships
    Technical details
    machine_predicate
    P61
    predicate_ref
    wikidata:property:P61
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:1:P61
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Pfaffian — named after → Johann Friedrich Pfaff — Observed provider relationships
    Technical details
    machine_predicate
    P138
    predicate_ref
    wikidata:property:P138
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:2:P138
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Pfaffian — instance of → mathematical concept — Observed provider relationships
    Technical details
    machine_predicate
    P31
    predicate_ref
    wikidata:property:P31
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:3:P31
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Pfaffian — Relationship label not yet available → 1852 — Observed provider relationships
    Technical details
    machine_predicate
    P575
    predicate_ref
    wikidata:property:P575
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:4:P575
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Pfaffian — different from → Pfaffian function — Observed provider relationships
    Technical details
    machine_predicate
    P1889
    predicate_ref
    wikidata:property:P1889
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:5:P1889
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Pfaffian — Relationship label not yet available → \operatorname{pf}(A)=\frac1{2^nn!} \sum_{\sigma \in S_{2n}}\operatorname{sgn}(\sigma) \prod _{i=1}^n A_{\sigma (2i-1),\sigma (2i)} — Observed provider relationships
    Technical details
    machine_predicate
    P2534
    predicate_ref
    wikidata:property:P2534
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:6:P2534
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Pfaffian — subclass of → determinant — Observed provider relationships
    Technical details
    machine_predicate
    P279
    predicate_ref
    wikidata:property:P279
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:7:P279
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • Johann Friedrich Pfaff — notable work → Pfaffian — Observed provider relationships
    Technical details
    machine_predicate
    P800
    predicate_ref
    wikidata:property:P800
    provider
    wikidata
    provider_direction
    incoming
    plane
    provider_observed
    edge_id
    wikidata:relation:8:P800
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

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    Unresolved references (0)

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