OAI/Combinatorics/SharpThreshold/SupportDegree.lean

GitHub source file

8 declarations, 0 contain sorry, 0 declared as axioms

Elementary support-graph combinatorics, independent of probability.

  1. def OAI.Problem313.SupportCombinatorics.vertices line 16

    Source documentation

    The non-isolated vertices of a finite edge family.

    def vertices (S : Finset (Finset α)) : Finset α := S.biUnion id
  2. def OAI.Problem313.SupportCombinatorics.degree line 19

    Source documentation

    The number of support edges incident to a vertex.

    def degree (S : Finset (Finset α)) (u : α) : ℕ :=
…
  3. lemma OAI.Problem313.SupportCombinatorics.edge_subset_vertices line 22
  4. lemma OAI.Problem313.SupportCombinatorics.card_vertices_le line 27
  5. lemma OAI.Problem313.SupportCombinatorics.degree_pos_iff line 35
  6. lemma OAI.Problem313.SupportCombinatorics.degree_le_card_vertices_sub_one line 39
  7. lemma OAI.Problem313.SupportCombinatorics.sum_degrees line 68
  8. lemma OAI.Problem313.SupportCombinatorics.exists_small_positive_degree line 88