All public logs
Jump to navigation
Jump to search
Combined display of all available logs of ProofWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 10:37, 15 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Matroid Bases Satisfy Formulation 3 of Matroid Base Axiom (Created page with "{{Proofread}} == Theorem == Let $M = \struct{S, \mathscr I}$ be a matroid. Let $\mathscr B$ be the set of bases of the matroid $M$. Then $\mathscr B$ satisfies formulation $3$ of base axiom: {{:User:Leigh.Samphier/Matroids/Axiom:Base Axiom (Matroid)/Formulation 3}} == Proof == <onlyinclude> </onlyi...")
- 09:23, 10 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Matroid Base Axiom (Created page with "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\mathscr B$ be a non-empty set of subsets of $S$. Then $\mathscr B$ is the set of bases of a matroid on $S$ {{iff}} $\mathscr B$ satisfies the base axiom: {{:User:Leigh.Samphier/Matroids/Axiom:Base Axio...")
- 09:17, 10 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 5 Iff Formulation 4 (content was: "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\mathscr B$ be a non-empty set of subsets of $S$. Then: :$\mathscr B$ satisfies formulation $5$ of base axiom: {{begin-axiom}} {{axiom | n = \text B 5 | q = \forall B_1, B_2 \in \mathscr B | mr= x \in B_1 \setminus B_2 \implies \exists y...")
- 09:05, 10 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 5 (Created page with "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\mathscr B$ be a non-empty set of subsets of $S$. Then: :$\mathscr B$ satisfies formulation $1$ of base axiom: {{:User:Leigh.Samphier/Matroids/Axiom:Base Axiom (Matroid)/Formulation 1}} {{iff}} :$\mathscr B$ satisfies User:Leigh.Samphier/Matr...")
- 08:47, 10 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 5 of Matroid Base Axiom/Lemma 1 (Created page with "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\mathscr B$ be a non-empty set of subsets of $S$ satisfying formulation $ of base axiom: {{:User:Leigh.Samphier/Matroids/Axiom:Base Axiom (Matroid)/Formulation 5}} Let $B_1, B_2 \in \mathscr B$. Let $U \subseteq B_1$ and $V \subseteq B_2$...")
- 22:53, 9 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 5 of Matroid Base Axiom/Sufficient Condition (Created page with "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\mathscr B$ be a non-empty set of subsets of $S$ satisfying formulation $ of base axiom: {{:User:Leigh.Samphier/Matroids/Axiom:Base Axiom (Matroid)/Formulation 5}} Then $\mathscr B$ is the set of bases of a ...")
- 22:52, 9 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 5 of Matroid Base Axiom/Necessary Condition (Created page with "{{Proofread}} == Theorem == Let $M = \struct {S, \mathscr I}$ be a matroid. Let $\mathscr B$ be the set of bases of the matroid $M$. Then $\mathscr B$ satisfies formulation $ of base axiom: {{:User:Leigh.Samphier/Matroids/Axiom:Base Axiom (Matroid)/Formulation 5}} == Proof == <onlyinclude> </onlyinclude>{{qed}} [...")
- 08:29, 8 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 3 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Larger Set has Larger Set Difference", and the only contributor was "Leigh.Samphier" (talk))
- 08:28, 8 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 5 (content was: "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $B_1, B_2 \subseteq S$. Let $z \in B_1 \setminus B_2$. Let $y \in B_2 \setminus B_1$. Let $B_3 = \paren{B_2 \setminus \set y} \cup \set z$ Then: <onlyinclude> :$\card{B_1 \cap B_3} = \card{B_1 \cap B_2} + 1$ </onlyinclude> == Proof == We have: {{begin-eqn}} {{eqn | l = B_3 \cap B_1 | r = \paren{\paren{B_2 \setminus \set y} \cup \set z} \cap B_1 }} {{eqn | r = \paren{\paren{B_2 \se...")
- 08:13, 8 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 4 (content was: "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $B_1, B_2, V \subseteq S$. Let $V \subseteq B_2$. Then: <onlyinclude> {{begin-eqn}} {{eqn | l = \card {B_1} | r = \card{B_1 \cap B_2} + \card{B_1 \setminus B_2} }} {{eqn | l = \card {B_2} | r = \card{B_2 \cap B_1} + \card{V \setminus B_1} + \card{\paren{B_2 \setminus B_1} \setminus V} }} {{end-eqn}} </onlyinclude> == Proof == We have: {{begin-eqn}} {{eqn | l = \card {B_1}...")
- 21:56, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 3 to User:Leigh.Samphier/Matroids/Larger Set has Larger Set Difference
- 12:47, 7 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 7 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 5 of Matroid Base Axiom/Lemma 2", and the only contributor was "Leigh.Samphier" (talk))
- 12:46, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 7 to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 5 of Matroid Base Axiom/Lemma 2
- 11:58, 7 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 5 of Matroid Base Axiom (Created page with "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\mathscr B$ be a non-empty set of subsets of $S$. Then $\mathscr B$ is the set of bases of a matroid on $S$ {{iff}} $\mathscr B$ satisfies the formulation 5 of base axiom: {{begin-axiom}}...")
- 11:22, 7 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 7 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 7", and the only contributor was "Leigh.Samphier" (talk))
- 11:20, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 7 to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 7
- 11:19, 7 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 5 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 5", and the only contributor was "Leigh.Samphier" (talk))
- 11:18, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 5 to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 5
- 11:15, 7 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 4 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 4", and the only contributor was "Leigh.Samphier" (talk))
- 11:14, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 4 to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 4
- 11:13, 7 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 3 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 3", and the only contributor was "Leigh.Samphier" (talk))
- 11:08, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 3 to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 3
- 10:44, 7 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 2 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 2", and the only contributor was "Leigh.Samphier" (talk))
- 10:39, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 2 to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 2
- 10:37, 7 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 1 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 1", and the only contributor was "Leigh.Samphier" (talk))
- 10:33, 7 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 1 to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Lemma 1
- 10:38, 6 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B4 Iff Axiom B5 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 5 Iff Formulation 4", and the only contributor was "Leigh.Samphier" (talk))
- 10:38, 6 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B1 Iff Axiom B3 (content was: "#REDIRECT User:User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 3", and the only contributor was "Leigh.Samphier" (talk))
- 10:37, 6 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B3 Iff Axiom B7 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 3 Iff Formulation 7", and the only contributor was "Leigh.Samphier" (talk))
- 10:34, 6 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B3 Iff Axiom B7 to User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 3 Iff Formulation 7
- 10:33, 6 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B1 Iff Axiom B4 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 4", and the only contributor was "Leigh.Samphier" (talk))
- 10:26, 6 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B4 Iff Axiom B5 to User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 5 Iff Formulation 4
- 10:23, 6 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B1 Iff Axiom B4 to User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 4
- 10:19, 6 May 2024 Leigh.Samphier talk contribs deleted page User:User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 3 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 3", and the only contributor was "Leigh.Samphier" (talk))
- 10:19, 6 May 2024 Leigh.Samphier talk contribs moved page User:User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 3 to User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 3
- 10:16, 6 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B1 Iff Axiom B3 to User:User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 3
- 08:45, 6 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/User:Leigh.Samphier/Matroids/Corollary of Set Difference Then Union Equals Union Then Set Difference (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Corollary of Set Difference Then Union Equals Union Then Set Difference", and the only contributor was "Leigh.Samphier" (talk))
- 08:45, 6 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/User:Leigh.Samphier/Matroids/Corollary of Set Difference Then Union Equals Union Then Set Difference to User:Leigh.Samphier/Matroids/Corollary of Set Difference Then Union Equals Union Then Set Difference
- 08:44, 6 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Exchange Subsets Between Sets (content was: "#REDIRECT User:Leigh.Samphier/Matroids/User:Leigh.Samphier/Matroids/Corollary of Set Difference Then Union Equals Union Then Set Difference", and the only contributor was "Leigh.Samphier" (talk))
- 08:42, 6 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 6 (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Exchange Subsets Between Sets", and the only contributor was "Leigh.Samphier" (talk))
- 08:40, 6 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Exchange Subsets Between Sets to User:Leigh.Samphier/Matroids/User:Leigh.Samphier/Matroids/Corollary of Set Difference Then Union Equals Union Then Set Difference
- 08:24, 6 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Exchange Subsets Between Sets to User:Leigh.Samphier/Matroids/Set Difference Then Union Equals Union Then Set Difference/Corollary
- 08:21, 6 May 2024 Leigh.Samphier talk contribs created page User:Leigh.Samphier/Matroids/Set Difference Then Union Equals Union Then Set Difference (Created page with "{{Proofread}} == Theorem == Let $S, A, B$ be sets. Let $A \subseteq S$. Let $A \cap B = \O$. Then: :$\paren{S \setminus A} \cup B = \paren{S \cup B} \setminus A$ == Proof == From Subsets of Disjoint Sets are Disjoint: :$A \cap B = \O$ From Set Difference with Disjoint Set: :$(1) \quad B \setminus A = B$ We have: {{begin-eqn}} {{eqn | l = \paren{S \cup B} \setminus A | r = \paren {S \setminus A} \cup \paren {B \setminus...")
- 22:28, 5 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Lemma 6 to User:Leigh.Samphier/Matroids/Exchange Subsets Between Sets
- 22:17, 5 May 2024 Leigh.Samphier talk contribs deleted page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B1 Implies Set of Matroid Bases (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Sufficient Condition", and the only contributor was "Leigh.Samphier" (talk))
- 22:15, 5 May 2024 Leigh.Samphier talk contribs moved page User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Axiom B1 Implies Set of Matroid Bases to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Sufficient Condition
- 22:14, 5 May 2024 Leigh.Samphier talk contribs deleted page User:User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Necessary Condition (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Necessary Condition", and the only contributor was "Leigh.Samphier" (talk))
- 22:11, 5 May 2024 Leigh.Samphier talk contribs deleted page User:User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom (content was: "#REDIRECT User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom", and the only contributor was "Leigh.Samphier" (talk))
- 22:10, 5 May 2024 Leigh.Samphier talk contribs moved page User:User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom
- 22:10, 5 May 2024 Leigh.Samphier talk contribs moved page User:User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Necessary Condition to User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Necessary Condition