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20 May 2024
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13:02 | User:Leigh.Samphier/Matroids/Matroid Bases Satisfy Formulation 3 of Matroid Base Axiom 6 changes history +824 [Leigh.Samphier (6×)] | |||
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13:02 (cur | prev) +230 Leigh.Samphier talk contribs | ||||
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| N 12:39 | User:Leigh.Samphier/Matroids/Subset Intersection Set DIfference is Empty Iff Subset of Second Set diffhist +236 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $S$ and $T$ be sets. Let $A \subseteq S$. Then: :$A \cap S \setminus T = \O$ {{iff}} $A \subseteq T$ == Proof == {{qed}} Category:Set Difference Category:Set Intersection") | ||||
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N 11:02 | User:Leigh.Samphier/Matroids/Independent Subset Contains No Dependent Subset/Corollary 3 5 changes history +709 [Leigh.Samphier (5×)] | |||
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11:02 (cur | prev) +4 Leigh.Samphier talk contribs | ||||
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08:17 (cur | prev) +384 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $M = \struct {S, \mathscr I}$ be a matroid. <onlyinclude> Let $B \subseteq S$ be any base of $M$. Then: :No circuit $C$ of $M$ is a subset of $B$. </onlyinclude> == Proof == {{qed}} Category:Matroid Bases Category:Matroid Circuits") | |||
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N 11:01 | User:Leigh.Samphier/Matroids/Independent Subset Contains No Dependent Subset/Corollary 2 5 changes history +782 [Leigh.Samphier (5×)] | |||
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11:01 (cur | prev) −10 Leigh.Samphier talk contribs | ||||
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08:15 (cur | prev) +425 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $M = \struct {S, \mathscr I}$ be a matroid. <onlyinclude> Let $X \subseteq S$ be any independent subset of $M$. Then: :No circuit $C$ of $M$ is a subset of $X$. </onlyinclude> == Proof == {{qed}} Category:Matroid Independent Subsets Category:Matroid Circuits") | |||
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N 11:00 | User:Leigh.Samphier/Matroids/Independent Subset Contains No Dependent Subset/Corollary 1 8 changes history +754 [Leigh.Samphier (8×)] | |||
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08:11 (cur | prev) +1 Leigh.Samphier talk contribs | ||||
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08:11 (cur | prev) +397 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $M = \struct {S, \mathscr I}$ be a matroid. Let $B \subseteq S$ be any base of $M$. Then: :No dependent subset $D$ of $M$ is a subset of $B$. == Proof == {{qed}} Category:Matroid Independent Subsets Category:Matroid Dependent Subsets") | |||
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N 11:00 | User:Leigh.Samphier/Matroids/Independent Subset Contains No Dependent Subset 9 changes history +1,418 [Leigh.Samphier (9×)] | |||
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08:06 (cur | prev) +426 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $M = \struct {S, \mathscr I}$ be a matroid. Let $X \subseteq S$ be any independent subset of $M$. Then: :No dependent subset $D$ of $M$ is a subset of $X$. == Proof == {{qed}} Category:Matroid Independent Subsets Category:Matroid Dependent Subsets") | |||
| N 08:23 | User:Leigh.Samphier/Matroids/Matroid Base Contains No Circuit diffhist +160 Leigh.Samphier talk contribs (Redirected page to User:Leigh.Samphier/Matroids/Independent Subset Contains No Dependent Subset/Corollary 3) | ||||
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N 08:21 | User:Leigh.Samphier/Matroids/Independent Subset Contains No Circuit 2 changes history +174 [Leigh.Samphier (2×)] | |||
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08:21 (cur | prev) 0 Leigh.Samphier talk contribs | ||||
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08:21 (cur | prev) +174 Leigh.Samphier talk contribs (Redirected page to User:Leigh.Samphier/Matroids/Independent Subset Contains No Dependent Subset/Corollary 1) Tag: New redirect | |||
19 May 2024
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22:21 | User:Leigh.Samphier/Matroids/Matroid Bases Satisfy Formulation 3 of Matroid Base Axiom 5 changes history +715 [Leigh.Samphier (5×)] | |||
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22:21 (cur | prev) +15 Leigh.Samphier talk contribs | ||||
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N 09:56 | User:Leigh.Samphier/Matroids/Matroid Bases Satisfy Formulation 3 of Matroid Base Axiom/Lemma 1 2 changes history +574 [Leigh.Samphier (2×)] | |||
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09:46 (cur | prev) +636 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $M = \struct{S, \mathscr I}$ be a matroid. Let $\mathscr C$ denote the set of circuits of $M$. <onlyinclude> Let $C_1, C_2, \ldots, C_n \in \mathscr C$ satisfy: :$(1) \quad \forall 0 \le i, j \le n : C_i \ne C_j$ :$(2) \quad \forall 0 \le k \le n : C_k \nsubseteq \ds \bigcup_{i \ne k} C_i$ Let: :$D \subseteq S : \size D < n$ Then: :$\exists C \in \mathscr C :...") | |||
15 May 2024
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N 10:50 | User:Leigh.Samphier/Matroids/Matroid Bases Satisfy Formulation 3 of Matroid Base Axiom 2 changes history +1,306 [Leigh.Samphier (2×)] | |||
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10:50 (cur | prev) +463 Leigh.Samphier talk contribs | ||||
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10:37 (cur | prev) +843 Leigh.Samphier talk contribs (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...") | |||
| 10:44 | User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms/Formulation 1 Iff Formulation 3 diffhist −607 Leigh.Samphier talk contribs | ||||
| 10:33 | User:Leigh.Samphier/Matroids/Matroid Bases Iff Satisfies Formulation 1 of Matroid Base Axiom/Sufficient Condition diffhist +9 Leigh.Samphier talk contribs | ||||