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

2001
*
Annals of Pure and Applied Logic
*

We present

doi:10.1016/s0168-0072(01)00091-4
fatcat:vqi32s5dmreqpi67b6b2fmtzdq
*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. ...##
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Smooth models of singular K3-surfaces
[article]

2017
*
arXiv
*
pre-print

As

arXiv:1608.06746v3
fatcat:so5m3d3eandmtcrjcirzgfaemy
*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 ...##
###
Coding Methods in Computability Theory and Complexity Theory
[article]

2013
*
arXiv
*
pre-print

We describe how

arXiv:1308.6399v1
fatcat:4kfitduebvddvoqaf3mw62equu
*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*. ...##
###
Face posets of tropical polyhedra and monomial ideals
[article]

2019
*
arXiv
*
pre-print

Their vertex-facet

arXiv:1909.01236v1
fatcat:ojlr7xbfqzh7dcykoyb2ydunf4
*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]. ...##
###
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*...

##
###
Twenty Female Mathematicians
[article]

2021
*
arXiv
*
pre-print

In fact,

arXiv:1910.01730v3
fatcat:2ftlzg73mncvtau6xlgu2ly264
*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 . ...##
###
Dynamics and processing in finite self-similar networks

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. ...

##
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Isogeny graphs with maximal real multiplication
[article]

2019
*
arXiv
*
pre-print

In his thesis, Kohel described

arXiv:1407.6672v4
fatcat:syv4rplqdvhvfmw6o3vxwf7grq
*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. ...##
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Resolutions and Cohomologies of Toric Sheaves. The affine case
[article]

2011
*
arXiv
*
pre-print

We study equivariant resolutions

arXiv:1106.5593v1
fatcat:njnam4qnwrhcpl42jhafjrsw4a
*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. ...##
###
The summer meeting in Seattle

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 ...

##
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FOUNDATIONS OF ONLINE STRUCTURE THEORY

2019
*
Bulletin of Symbolic Logic
*

Let

doi:10.1017/bsl.2019.20
fatcat:7cs7fag7cjcwdehdo6ji2qd5vu
*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 ...##
###
Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

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

doi:10.21468/scipostphys.9.6.083
fatcat:5g7jppkudrcxdjdwm6kbe5aofu
*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. ...##
###
Classification of all 𝒩≥ 3 moduli space orbifold geometries at rank 2
[article]

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

arXiv:1904.10969v2
fatcat:qenxq7k4wzcgzgkf7muso5hdxe
*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. ...##
###
Algebraic and Geometric Methods in Enumerative Combinatorics
[chapter]

2015
*
Handbook of Enumerative Combinatorics
*

I am very grateful to Miklós Bóna

doi:10.1201/b18255-3
fatcat:du3dolwwkra73brq2hcesgu42q
*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. ...##
###
Algebraic and geometric methods in enumerative combinatorics
[article]

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. ...

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