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A proof of the matrix version of Baker's conjecture in Diophantine approximation

TUSHAR DAS, DAVID SIMMONS
2018 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
AbstractWe prove that the matrix analogue of the Veronese curve is strongly extremal in the sense of Diophantine approximation, thereby resolving a question posed by Beresnevich, Kleinbock and Margulis  ...  The first-named author was supported in part by a 2016-2017 Faculty Research Grant from the University of Wisconsin-La Crosse.  ...  The research of the secondnamed author was supported in part by the EPSRC Programme Grant EP/J018260/1.  ... 
doi:10.1017/s0305004118000269 fatcat:gnau54kd45hs3frbxrz5udcdam

The Merrifield-Simmons Conjecture Holds for Bipartite Graphs

Martin Trinks
2012 Journal of Graph Theory  
Then the Merrifield-Simmons conjecture states that the sign of the term σ(G_-u) ·σ(G_-v) - σ(G) ·σ(G_-u-v) only depends on the parity of the distance of the vertices u, v ∈ V in G.  ...  We prove that the conjecture holds for bipartite graphs by considering a generalization of the term, where vertex subsets instead of vertices are deleted.  ...  Hence we want to generalize the Merrifield-Simmons conjecture by asking for which graphs and which vertex sets the following conjecture holds: Conjecture 3 (generalized Merrifield-Simmons conjecture).  ... 
doi:10.1002/jgt.21656 fatcat:4jouodefhrcbjb5hjnzpxxevie

The Merrifield-Simmons conjecture also holds for parity graphs [article]

Martin Trinks
2014 arXiv   pre-print
The Merrifield-Simmons conjectures states a relation between the distance of vertices in a simple graph G and the number of independent sets, denoted as σ(G), in vertex-deleted subgraphs.  ...  Namely, that the sign of the term σ(G_-u) ·σ(G_-v) - σ(G) ·σ(G_-u-v) only depends on the parity of the distance of u and v in G.  ...  The Merri eld-Simmons conjecture holds for parity graphs.  ... 
arXiv:1401.1596v1 fatcat:yptjkv3vdncldmjxoe6xrpcosy

Page 40 of Georgia. Supreme Court. Reports of Cases in Law and Equity Argued and Determined in the Supreme Court of Georgia Vol. 14, Issue [page]

1853 Georgia. Supreme Court. Reports of Cases in Law and Equity Argued and Determined in the Supreme Court of Georgia  
Probability, inference and conjecture, drawn en- tirely from parol proof, and that of the vaguest character, are  ...  It is in proof by Mr. Simmons, that he issued them. They furnish the written evidence of service. To rebut this, the strongest testimony should’ be required.  ... 

Mr. Smith, on the Cutting Gorget

Thomas Smith
1809 The Medical and physical journal  
Simmons should choose for himself, success as a criterion of the fitness of that instrument.  ...  And here I may be allowed to digress, as a very material circumstance invites discussion, or at least, inquiry. This is, what description of proof Mr. Simmons's irrefragable proof is?  ... 
pmid:30492746 pmcid:PMC5697242 fatcat:ixne5432kvefzbc6krrcogetx4

Page 333 of Critical Review; Or, Annals of Literature Vol. 14, Issue 3 [page]

1808 Critical Review; Or, Annals of Literature  
These commentators have not been able to advance a single proof in support of their accusation.  ...  But they have all endea- youred to supply the place of proof by bold assumptions, faint al- lusions, forced constructions, and improbable conjectures.  ... 

The Borsuk–Ulam-property, Tucker-property and constructive proofs in combinatorics

Mark de Longueville, Rade T. Živaljević
2006 Journal of combinatorial theory. Series A  
This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far.  ...  To this end the combinatorial concept of Tucker-property of a finite group G is introduced and its relation to the topological Borsuk-Ulam-property is discussed.  ...  This also relates to a conjecture of Simmons and Su, which we will discuss as well.  ... 
doi:10.1016/j.jcta.2005.08.002 fatcat:2efmuomnaveyzecgpwx65vwkpa

Page 1972 of Mathematical Reviews Vol. , Issue 90D [page]

1990 Mathematical Reviews  
The following is a sketch of the proof of (a).  ...  modified version of Simmons’ criterion).  ... 

Page 28 of Mathematical Reviews Vol. , Issue 82a [page]

1982 Mathematical Reviews  
Heawood’s map-colouring conjecture. The Ringel- Youngs proof of the Heawood conjecture [G. Ringel and J. W. T. Youngs, Proc. Nat. Acad. Sci.  ...  However, some of these lemmas can be used in a different way, to give a ‘graph- theoretic’ proof of Tutte’s excluded minor characterization of graphic matroids, and in this paper we explain how.” W.  ... 

Arrangements of Lines with a Large Number of Triangles

Z. Furedi, I. Palasti
1984 Proceedings of the American Mathematical Society  
An arrangement of lines is constructed by choosing n diagonals of the regular 2/i-gon. This arrangement is proved to form at least n(n -3)/3 triangular cells.  ...  Proof. Ha+ß+y=0 (mod27r), then the sum of lengths of (directed) arcs (P(a), P(y)) and (P(ß), P(ir -2y)) is equal to it. This implies that L(y) is perpendicular to the fine P(a) P(ß).  ...  The proof is easy. 6. The orchard problem. Given a vertex V in an arrangement si, denote by t(V, si) the multiplicity of V, i.e. the number of lines of ^incident to V.  ... 
doi:10.2307/2045427 fatcat:7f6j5jmsqnahrbhiyxim4wzjt4

Arrangements of lines with a large number of triangles

Z. F{üredi, I. Pal{ásti
1984 Proceedings of the American Mathematical Society  
An arrangement of lines is constructed by choosing n diagonals of the regular 2/i-gon. This arrangement is proved to form at least n(n -3)/3 triangular cells.  ...  Proof. Ha+ß+y=0 (mod27r), then the sum of lengths of (directed) arcs (P(a), P(y)) and (P(ß), P(ir -2y)) is equal to it. This implies that L(y) is perpendicular to the fine P(a) P(ß).  ...  The proof is easy. 6. The orchard problem. Given a vertex V in an arrangement si, denote by t(V, si) the multiplicity of V, i.e. the number of lines of ^incident to V.  ... 
doi:10.1090/s0002-9939-1984-0760946-2 fatcat:wjakd32wbzhhxlvqnebxpu4x6e

On arithmetic progressions in self-similar sets [article]

Kan Jiang, Qiyang Pei, Lifeng Xi
2019 arXiv   pre-print
Given a sequence {b_i}_i=1^n and a ratio λ∈ (0,1), let E=∪_i=1^n(λ E+b_i) be a homogeneous self-similar set. In this paper, we study the existence and maximal length of arithmetic progressions in E.  ...  Acknowledgements The work is supported by National Natural Science Foundation of China (Nos. 11831007, 11771226, 11701302, 11371329, 11471124, 11671147). The work is also supported by K.C.  ...  Therefore, he obtained a new proof of Szemerédi's theorem, for a survey of this topic, see [21] . It is natural to investigate to a subset of natural numbers which is of zero density.  ... 
arXiv:1901.06673v1 fatcat:33rbz5y3hbfc5az3pqtwhv3svu

Topological chirality of certain molecules

Jonathan Simon
1986 Topology  
It is conjectured in [S] and [9] that the Simmons-Paquette KS molecule is topologically chiral; the methods of Section II provide the desired proof. THEOREM 111.1.  ...  CHIRALITY OF A .MOLECULAR K5 Fig. 7 . 7 synthesized independently in 1981 by H. Simmons et al. and L. A. Paquette et al.  ... 
doi:10.1016/0040-9383(86)90041-8 fatcat:poiaf7uedzf6dak5m2nzq24rxu

The chromatic number of the sphere

Gustavus J. Simmons
1976 Journal of the Australian Mathematical Society  
One of Erdos' long standing conjectures is that / y(S») = 4.  ...  Simmons (1974) disproved this by showing 4 S x(^</V3) while Straus  ...  It seems appropriate to close with two new conjectures about the chromatic number of the sphere and a reiteration of Erdos' open conjecture on the chromatic number of the plane: x = \ at the values of  ... 
doi:10.1017/s1446788700019315 fatcat:krmjr3ygr5fh3gurfpnxrxilxa

Christoffel-Darboux type identities for independence polynomial [article]

Ferenc Bencs
2014 arXiv   pre-print
Another application is related to a conjecture of Merrifield and Simmons.  ...  As an application, we give a new proof of a theorem of M. Chudnovsky and P. Seymour, claiming that the independence polynomial of a claw-free graph has only real roots.  ...  I would like to express my sincere gratitude to Péter Csikvári for introducing me a set of problems which led to this paper.  ... 
arXiv:1409.2527v1 fatcat:xt5smgioavdbfgug7teilnee4q
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