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MINIMAL EXPANSIONS OF SEMILATTICES

2004
*
International journal of algebra and computation
*

The results involve the investigation

doi:10.1142/s0218196704001852
fatcat:k4skwofk3jatrk2xbfvfkh6lfm
*of*some*minimal**expansions**of**semilattices*. ... We determine the*minimal*extension*of*the sequence 0, 1, 1, . . . , 1, 2 . This completes and extends the work*of*K. M. ... On the basis*of*this lemma, we will refer to an algebra that represents the length m + 1 sequence 0, 1, . . . , 1, 2 as an m-ary*semilattice**expansion*. ...##
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Page 205 of Mathematical Reviews Vol. , Issue 2000a
[page]

2000
*
Mathematical Reviews
*

Once again the particular case

*of**semilattices*leads to an*expansion*which corresponds to a known*expansion*$2) due to K. Henckell. ... The so-called Karnofsky-Rhodes*expansion*fits under this heading, while expanding by the variety*of**semilattices*is the same as applying the Cayley*expansion*. ...##
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Page 6368 of Mathematical Reviews Vol. , Issue 2002I
[page]

2002
*
Mathematical Reviews
*

An example

*of*a planar, rank-connected lattice that is not admissible is given.” 2002i:06004 06A12 06A06 McElwee, Brett (5-SYD-SM; Sydney) Maximal and*minimal**semilattices*on ordered sets. ... non-*expansive*multiplier; (2) f is a multiplicative operator; (3) f isa quasi-interior operator. ...##
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Medians, lattices, and trees

1954
*
Proceedings of the American Mathematical Society
*

In other papers [3; 4]2 the author discussed the behavior

doi:10.1090/s0002-9939-1954-0064750-3
fatcat:zbsahadv2ne6jfcccyyyxrblrm
*of*medians, segments, and betweenness in systems called median*semilattices*. A tree is a type*of*median*semilattice*. ... In a*semilattice*an upper bound*of*a and b is an element / such that a=at and b = bt. ... The extension T*of*5 which has been described is*minimal*in the sense that a distributive lattice containing 5 contains a sublattice isomorphic to T. ...##
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Page 06 of Mathematical Reviews Vol. , Issue 90C
[page]

1990
*
Mathematical Reviews
*

The

*minimal*k with the above property is called the Boolean dimension dima,(P)*of*P. We present a universal upper bound for the Boolean dimen- sion*of*posets. ... The blocks*of*the inverse matrix immediately give the wanted*expansion*. Heinrich Niederhausen (1-FLAT) 90c:06007 06A10 Rus, Ioan A. ...##
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Monads and Quantitative Equational Theories for Nondeterminism and Probability

2020
*
International Conference on Concurrency Theory
*

Our main result is the presentation

doi:10.4230/lipics.concur.2020.28
dblp:conf/concur/MioV20
fatcat:lxbn2qhbffht5kto36awdzsvqm
*of*this lifted monad in terms*of*the quantitative equational theory*of*convex*semilattices*, using the framework*of*quantitative algebras recently introduced by Mardare ... The monad*of*convex sets*of*probability distributions is a well-known tool for modelling the combination*of*nondeterministic and probabilistic computational effects. ... We need to verify that F(f ) is a morphisms in QA(QTh CS ), i.e., a non-*expansive*homomorphism*of*convex*semilattices*(see Definition 22) . ...##
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Monads and Quantitative Equational Theories for Nondeterminism and Probability
[article]

2020
*
arXiv
*
pre-print

Our main result is the presentation

arXiv:2005.07509v1
fatcat:4oqtddfruvfurkga7h6nrmwg5y
*of*this lifted monad in terms*of*the quantitative equational theory*of*convex*semilattices*, using the framework*of*quantitative algebras recently introduced by Mardare ... The monad*of*convex sets*of*probability distributions is a well-known tool for modelling the combination*of*nondeterministic and probabilistic computational effects. ... We want to prove that whenever f : ((X, d), α) → ((Y, d ), β) is a non-*expansive*morphism*of*Eilenberg-Moore algebras then F(f ) is a non-*expansive*homomorphism*of*convex*semilattices*. ...##
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Page 63 of Mathematical Reviews Vol. , Issue 91K
[page]

1991
*
Mathematical Reviews
*

The author studies the convexity structure in the space

*of*all order arcs*of*a*semilattice*. He obtains three main theorems. ... The first gives some simple conditions under which an arc*of*a*semilattice*is mapped back into itself by an order-preserving function. ...##
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The Ramsey and the ordering property for classes of lattices and semilattices
[article]

2018
*
arXiv
*
pre-print

It now comes as no surprise that the same is true for varieties

arXiv:1802.00979v1
fatcat:frmcij5yjjedtelqw4b3zq7nxq
*of**semilattices*. ... We show that for almost all nontrivial locally finite varieties*of*lattices no "reasonable"*expansion**of*the finite members*of*the variety by linear orders gives rise to a Ramsey class. ... The author gratefully acknowledges the support*of*the Ministry*of*Science, Education and Technological Development*of*the Republic*of*Serbia, Grant No. 174019. ...##
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Page 158 of Mathematical Reviews Vol. , Issue 90A
[page]

1990
*
Mathematical Reviews
*

*Minimal*non-finitely based varieties are called limit varieties. All previously discovered limit varieties

*of*semigroups are homotypical (contain the variety

*of*

*semilattices*). ... An

*expansion*

*of*S (or, more precisely, an

*expansion*

*of*the morphism /: A* — S, where f denotes the free semigroup on A) is a morphism g: A* — T such that f = hg for some surjective morphism /: T — S. ...

##
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The median function on median graphs and semilattices

2000
*
Discrete Applied Mathematics
*

In this paper a new characterization

doi:10.1016/s0166-218x(99)00208-5
fatcat:ve72ryvzcfcephqrsepmxq5ace
*of*the median function is given for G a median graph. This is used to give a characterization*of*the median function on median*semilattices*. ? ... A median*of*a k-tuple = (x 1; : : : ; x k )*of*vertices*of*a ÿnite connected graph G is a vertex x for which k i=1 d(x; xi) is minimum, where d is the geodesic metric on G. ... An important feature which follows from the proof*of*Theorem 1 is that in obtaining a graph G from a median graph H by a succession*of**expansions*, the*expansions*can be applied in any order. ...##
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Page 2396 of Mathematical Reviews Vol. , Issue 87e
[page]

1987
*
Mathematical Reviews
*

For instance, S is a left group if and only if B(S) is a left zero band; S is a

*semilattice**of*groups if and only if B(S) is a commutative regular semigroup (or, equivalently, B(S) is a*semilattice*). ... The*minimal*right congruences*of*a semigroup are classified into three types 21, N2, N3 according to the conditions (1), (2), (3). ...##
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On semilattices and lattices for families of theories
[article]

2017
*
arXiv
*
pre-print

We define and study

arXiv:1701.00208v2
fatcat:3wwi7i2htndvnb2ti4fnmyv72u
*semilattices*and lattices for E-closed families*of*theories. Properties*of*these*semilattices*and lattices are investigated. ... It is shown that lattices for families*of*theories with least generating sets are distributive. ... By the definition, an e-*minimal*structure A ′ consists*of*E-classes with a*minimal*set TH(A ′ ). If TH(A ′ ) is the least for models*of*Th(A ′ ) then A ′ is called e-least. Definition [2] . ...##
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On tolerances representable as R ∘ R^-
[article]

2006
*
arXiv
*
pre-print

(ii) Consider the

arXiv:math/0610091v1
fatcat:3vad55pyivb47olyuxzcbknzoy
*semilattice*S with 6*minimal*elements a, b 1 , b 2 , b 3 , b 4 , c and with a largest element 1. ... If x, y are*minimal*elements*of*S and both x R 1 and y R 1, then x R • R − y, hence x Θ y. ...##
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Recent Results on the Algebraic Approach to the CSP
[chapter]

2008
*
Lecture Notes in Computer Science
*

We describe an algebraic approach to the constraint satisfaction problem (CSP) and present recent results on the CSP that make use

doi:10.1007/978-3-540-92800-3_4
fatcat:x56vxo4fobadjmeayv3k35atgi
*of*, in an essential way, this algebraic framework. ... ; a contradiction with*minimality**of*B. ... Let A be a finite algebra and α a*minimal*congruence*of*A. ...
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