Conjecture and proof / by 181611 Laczkovich, Miklos

Serre's conjectures / by 341890 Alam, T. Y.

The Delta Conjecture by James Haglund, Jeffrey B. Remmel, Andrew Timothy Wilson

“…Both interpretations can be seen as generalizations of the Shuffle Conjecture, a statement originally conjectured by Haglund, Haiman, Remmel, Loehr, and Ulyanov and recently proved by Carlsson and Mellit. …”
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On the Cîrtoaje’s conjecture by Ladislav Matejíčka

“…Abstract In this paper, we prove the Cîrtoaje conjecture under other conditions.…”
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On the composition conjectures by Mohamad A. M. Alwash

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The Rearrangement Conjecture by Jay Pantone, Vincent Vatter

“…The Rearrangement Conjecture states that if two words over $\mathbb{P}$ are Wilf-equivalent in the factor order on $\mathbb{P}^{\ast}$ then they are rearrangements of each other. …”
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On Ryser's conjecture by Haxell, P, Scott, A

“…Motivated by an old problem known as Ryser's Conjecture, we prove that for r = 4 and r = 5, there exists ∈ > 0 such that every r-partite r-uniform hypergraph H has a cover of size at most (r - ∈)v(H), where v(H) denotes the size of a largest matching in H.…”

The Duchet conjecture by Prakash, V., Parthasarathy, K. R., Rangan, C. Pandu

“…In this paper, we investigate a conjecture of Duchet that r(G)≤η(G)+1, where r(G) is the Radon number and η(G) is the Hadwiger number of a graph G. …”
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The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs by Cranston Daniel W., Jahanbekam Sogol, West Douglas B.

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On a combination of the 1-2-3 Conjecture and the Antimagic Labelling Conjecture by Julien Bensmail, Mohammed Senhaji, Kasper Szabo Lyngsie

Subjects: “…1-2-3 conjecture…”
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Conjectures on Foam Mobilization Conjectures sur la mobilisation des mousses by De Gennes P. G.

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Generic Beauville’s Conjecture by Izzet Coskun, Eric Larson, Isabel Vogt

“…We prove this conjecture if the map $\alpha $ is general in any component of the Hurwitz space of covers of an arbitrary smooth curve Y.…”
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The Topological Entropy Conjecture by Lvlin Luo

“…Then, we prove the conjecture <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">log</mo><mi>ρ</mi><mo>≤</mo><mi>e</mi><mi>n</mi><msub><mi>t</mi><mi>L</mi></msub><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> for <i>f</i> being a continuous self-map on a given compact Hausdorff space <i>X</i>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> is the maximum absolute eigenvalue of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>f</mi><mo>*</mo></msub></semantics></math></inline-formula>, which is the linear transformation associated with <i>f</i> on the Čech homology group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mover accent="true"><mi>H</mi><mo>ˇ</mo></mover><mo>*</mo></msub><mrow><mo>(</mo><mi>X</mi><mo>;</mo><mi mathvariant="double-struck">Z</mi><mo>)</mo></mrow><mo>=</mo><mstyle displaystyle="true"><munderover><mo>⨁</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></munderover></mstyle><mrow><msub><mover accent="true"><mi>H</mi><mo>ˇ</mo></mover><mi>i</mi></msub><mrow><mo>(</mo><mi>X</mi><mo>;</mo><mi mathvariant="double-struck">Z</mi><mo>)</mo></mrow></mrow><mo>.…”
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On the B-Semiampleness Conjecture by Enrica Floris, Vladimir Lazić

“…The B-Semiampleness Conjecture of Prokhorov and Shokurov predicts that the moduli part in a canonical bundle formula is semiample on a birational modification. …”
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On two Kuznetsov’s conjectures by Florian Oschmann

“…We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.…”
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On the Grone-Merris conjecture by Tamon Stephen

“…We prove that this conjecture holds for a class of graphs including trees. …”
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On a conjecture of Erdős by Chen, Yong-Gao, Ding, Yuchen

“…In this note, we confirm an old conjecture of Erdős.…”
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On Comon’s and Strassen’s Conjectures by Alex Casarotti, Alex Massarenti, Massimiliano Mella

Subjects: “…Strassen’s conjecture…”
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Another Antimagic Conjecture by Rinovia Simanjuntak, Tamaro Nadeak, Fuad Yasin, Kristiana Wijaya, Nurdin Hinding, Kiki Ariyanti Sugeng

“…We also provide evidence that the conjecture is true. We present computational results that, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula>, all graphs of order up to 8 concur with the conjecture. …”
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The maximal rank conjecture by Larson, Eric Kerner

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