All collections and the maps between them
Dyck path --> Permutation Standard tableau --> Permutation Set partition --> Permutation Binary tree --> Permutation Perfect matching --> Permutation Alternating sign matrix --> Permutation Semistandard tableau --> Permutation Parking function --> Permutation Permutation --> Integer partition Dyck path --> Integer partition Integer composition --> Integer partition Standard tableau --> Integer partition Set partition --> Integer partition Core --> Integer partition Poset --> Integer partition Semistandard tableau --> Integer partition Graph --> Integer partition Binary tree --> Dyck path Alternating sign matrix --> Dyck path Ordered tree --> Dyck path Parking function --> Dyck path Permutation --> Integer composition Dyck path --> Integer composition Parking function --> Integer composition Binary word --> Integer composition Dyck path --> Standard tableau Perfect matching --> Set partition Ordered tree --> Binary tree Alternating sign matrix --> Perfect matching Permutation --> Poset Binary tree --> Poset Ordered tree --> Poset Standard tableau --> Gelfand-Tsetlin pattern Semistandard tableau --> Gelfand-Tsetlin pattern Alternating sign matrix --> Semistandard tableau Binary tree --> Graph Poset --> Graph Ordered tree --> Graph Permutation --> Binary word Integer partition --> Binary word Dyck path --> Binary word Permutations Integer partitions Dyck paths Integer compositions Standard tableaux Set partitions Binary trees Perfect matchings Cores Posets Alternating sign matrices Gelfand-Tsetlin patterns Semistandard tableaux Graphs Ordered trees Parking functions Binary words