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A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees preserving greatest element

Burkhard Englert
2001 Annals of Pure and Applied Logic  
We present a necessary and su cient condition for the embeddability of a ÿnite principally decomposable lattice into the computably enumerable degrees preserving greatest element.  ...  The author is grateful to his thesis advisor Manuel Lerman for many valuable comments and suggestions.  ...  Acknowledgements The results in this paper are part of the author's Ph.D. Dissertation [7] at the University of Connecticut.  ... 
doi:10.1016/s0168-0072(01)00091-4 fatcat:vqi32s5dmreqpi67b6b2fmtzdq

Smooth models of singular K3-surfaces [article]

Alex Degtyarev
2017 arXiv   pre-print
As a by-product, we observe a correlation (up to a certain limit) between the discriminant of a singular K3-surface and the number of lines in its models.  ...  We also construct a K3-quartic surface with 52 lines and singular points, as well as a few other examples with many lines or models.  ...  It is shown in [5] that rk Z 52 = 19 and Z 52 admits a unique, up to isomorphism preserving h, embedding into L = H 2 (X); the orthogonal complement Z ⊥ 52 is the rank 3 lattice W with the Gram matrix  ... 
arXiv:1608.06746v3 fatcat:so5m3d3eandmtcrjcirzgfaemy

Coding Methods in Computability Theory and Complexity Theory [article]

Andre Nies
2013 arXiv   pre-print
We describe how a similar program can be carried out for several other structures, including the structure of c.e. many one degrees, the structure of c.e. weak truth table degrees and the lattice of c.e  ...  A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success.  ...  ♦ For x, y ∈ D, we write nd[x, y] if x < y and the interval [x, y] does not embed the 4-element boolean algebra preserving least and greatest element.  ... 
arXiv:1308.6399v1 fatcat:4kfitduebvddvoqaf3mw62equu

Face posets of tropical polyhedra and monomial ideals [article]

Georg Loho, Ben Smith
2019 arXiv   pre-print
Their vertex-facet lattice is homotopy equivalent to a sphere and encodes the Betti numbers of an associated monomial ideal.  ...  We focus on monomial tropical polyhedra, and deduce how their geometry reflects properties of monomial ideals.  ...  Moreover, DM (P ) is the smallest complete lattice that P embeds into: any embedding P ֒→ L into a complete lattice L induces an embedding DM (P ) ֒→ L [49, Theorem 5.3.8].  ... 
arXiv:1909.01236v1 fatcat:ojlr7xbfqzh7dcykoyb2ydunf4

Abstracts of papers

1938 Bulletin of the American Mathematical Society  
A necessary and sufficient condition that the functions shall have a linear regression system is derived.  ...  Necessary and sufficient conditions that such rji form a linearly independent base relative to M are: (1) for every g** there is one and only one ijj such that g H is minimum for g H (M)yii -0\ (2) the  ... 
doi:10.1090/s0002-9904-1938-06672-4 fatcat:6wvhi2aa65dtdfrvdqrco42xuq

Twenty Female Mathematicians [article]

Hollis Williams
2021 arXiv   pre-print
In fact, the main use will probably be for a student who is coming to a new area of mathematics for the first time and needs an overview of some of the key results and references viewed through the work  ...  The work may be useful as a historical resource, but there is very little biography or history, and the primary focus is on the mathematics.  ...  A finite extension is one with finite degree and an extension (denoted as ∶ ) is algebraic if every element of is algebraic over .  ... 
arXiv:1910.01730v3 fatcat:2ftlzg73mncvtau6xlgu2ly264

Dynamics and processing in finite self-similar networks

S. DeDeo, D. C. Krakauer
2012 Journal of the Royal Society Interface  
A common feature of biological networks is the geometric property of self-similarity.  ...  We analyze the relationship between topology and signaling in contrasting classes of such topologies.  ...  However, a general algorithm for the computation of an arbitrary P q,fag,fbg may be specified. One decomposes the problem into two parts.  ... 
doi:10.1098/rsif.2011.0840 pmid:22378750 pmcid:PMC3405736 fatcat:fctem34dozeanjav5rj22upgye

Isogeny graphs with maximal real multiplication [article]

Sorina Ionica
2019 arXiv   pre-print
In his thesis, Kohel described the structure of isogeny graphs for elliptic curves and showed that one may compute the endomorphism ring of an elliptic curve defined over a finite field by using a depth  ...  Over finite fields, we derive a depth first search algorithm for computing endomorphism rings locally at prime numbers, if the real multiplication is maximal.  ...  We are indebted to John Boxall for sharing his ideas regarding the computation of isogenies preserving the real multiplication, and providing guidance for improving the writing of this paper.  ... 
arXiv:1407.6672v4 fatcat:syv4rplqdvhvfmw6o3vxwf7grq

Resolutions and Cohomologies of Toric Sheaves. The affine case [article]

Markus Perling
2011 arXiv   pre-print
We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules  ...  for the general case.  ...  For conversations which brought new ideas into this project I want to thank Günther Trautmann, Henning Krause, Ezra Miller, and Vic Reiner. Overview of the paper.  ... 
arXiv:1106.5593v1 fatcat:njnam4qnwrhcpl42jhafjrsw4a

The summer meeting in Seattle

V. L. Klee Jr.
1956 Bulletin of the American Mathematical Society  
Necessary and sufficient conditions are given under which B may be imbedded into a Banach lattice X so that $(e) coincides with the norm of X on B.  ...  The paper presents new necessary and sufficient conditions for globality of certain subsets of 5 n .  ...  Consider the differential equation (1) x(0) =c where $(x) is a continuous function of x satisfying additional conditions ensuring the existence of a unique solution over the interval O^t^T for a ^c  ... 
doi:10.1090/s0002-9904-1956-10067-0 fatcat:psguzmtiurgxxaranalbw7fh2y

FOUNDATIONS OF ONLINE STRUCTURE THEORY

NIKOLAY BAZHENOV, ROD DOWNEY, ISKANDER KALIMULLIN, ALEXANDER MELNIKOV
2019 Bulletin of Symbolic Logic  
Let A be a f.g. rigid punctual structure with P R(A) infinite, and let L be a countable lattice. TFAE: (1) L is embeddable into P R(A) preserving sup and inf; (2) L is distributive.  ...  Szemeredi and others showed that there is a computable partial ordering of width k that cannot be decomposed into k computable chains.  ...  There is a primitive recursive function i(n) such that for every n the function p i(n) = ϕ l(i(n)) is the time function for p n = ϕ l(n) with respect to the uniformly primitive recursive approximation  ... 
doi:10.1017/bsl.2019.20 fatcat:7cs7fag7cjcwdehdo6ji2qd5vu

Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

Philip Argyres, Antoine Bourget, Mario Martone
2020 SciPost Physics  
Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an \mathcal{N}=2𝒩=2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence  ...  The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them.  ...  Acknowledgments It is a pleasure to thank Jacques Distler, Behzat Ergun, Amihay Hanany, Carlo Meneghelli, Elli Pomoni and Leonardo Rastelli for useful discussions.  ... 
doi:10.21468/scipostphys.9.6.083 fatcat:5g7jppkudrcxdjdwm6kbe5aofu

Classification of all 𝒩≥ 3 moduli space orbifold geometries at rank 2 [article]

Philip C. Argyres, Antoine Bourget, Mario Martone
2020 arXiv   pre-print
Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an 𝒩=2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic  ...  The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them.  ...  A The Du Val nomenclature We describe the finite subgroups of U(2) that are used in the text. We adopt the notation introduced by Du Val in [29] , and summarized in Table 12.  ... 
arXiv:1904.10969v2 fatcat:qenxq7k4wzcgzgkf7muso5hdxe

Algebraic and Geometric Methods in Enumerative Combinatorics [chapter]

Federico Ardila
2015 Handbook of Enumerative Combinatorics  
I am very grateful to Miklós Bóna for the invitation to contribute to this project.  ...  I also thank Alex Fink, Alicia Dickenstein, Alin Bostan, David Speyer, Federico Castillo, Mark Wildon, Richard Stanley, and the anonymous referee for their helpful comments.  ...  Lattices A poset is a lattice if every two elements p and q have a least upper bound p ∨ q and a greatest lower bound p ∧ q, called their meet and join, respectively.  ... 
doi:10.1201/b18255-3 fatcat:du3dolwwkra73brq2hcesgu42q

Algebraic and geometric methods in enumerative combinatorics [article]

Federico Ardila
2015 arXiv   pre-print
A survey written for the upcoming "Handbook of Enumerative Combinatorics".  ...  I am very grateful to Miklós Bóna for the invitation to contribute to this project.  ...  I also thank Alex Fink, Alicia Dickenstein, Alin Bostan, David Speyer, Federico Castillo, Mark Wildon, Richard Stanley, and the anonymous referee for their helpful comments.  ... 
arXiv:1409.2562v2 fatcat:k46fzxiawnfrhjafnqstj4sifu
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