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MINIMAL EXPANSIONS OF SEMILATTICES

P. JIPSEN, A. KISIELEWICZ
2004 International journal of algebra and computation  
The results involve the investigation 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.  ... 
doi:10.1142/s0218196704001852 fatcat:k4skwofk3jatrk2xbfvfkh6lfm

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.  ... 

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.  ... 

Medians, lattices, and trees

Marlow Sholander
1954 Proceedings of the American Mathematical Society  
In other papers [3; 4]2 the author discussed the behavior 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.  ... 
doi:10.1090/s0002-9939-1954-0064750-3 fatcat:zbsahadv2ne6jfcccyyyxrblrm

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.  ... 

Monads and Quantitative Equational Theories for Nondeterminism and Probability

Matteo Mio, Valeria Vignudelli, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
Our main result is the presentation 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) .  ... 
doi:10.4230/lipics.concur.2020.28 dblp:conf/concur/MioV20 fatcat:lxbn2qhbffht5kto36awdzsvqm

Monads and Quantitative Equational Theories for Nondeterminism and Probability [article]

Matteo Mio, Valeria Vignudelli
2020 arXiv   pre-print
Our main result is the presentation 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.  ... 
arXiv:2005.07509v1 fatcat:4oqtddfruvfurkga7h6nrmwg5y

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.  ... 

The Ramsey and the ordering property for classes of lattices and semilattices [article]

Dragan Mašulović
2018 arXiv   pre-print
It now comes as no surprise that the same is true for varieties 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.  ... 
arXiv:1802.00979v1 fatcat:frmcij5yjjedtelqw4b3zq7nxq

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.  ... 

The median function on median graphs and semilattices

F.R. McMorris, H.M. Mulder, R.C. Powers
2000 Discrete Applied Mathematics  
In this paper a new characterization 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.  ... 
doi:10.1016/s0166-218x(99)00208-5 fatcat:ve72ryvzcfcephqrsepmxq5ace

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).  ... 

On semilattices and lattices for families of theories [article]

Sergey V. Sudoplatov
2017 arXiv   pre-print
We define and study 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] .  ... 
arXiv:1701.00208v2 fatcat:3wwi7i2htndvnb2ti4fnmyv72u

On tolerances representable as R ∘ R^- [article]

Paolo Lipparini
2006 arXiv   pre-print
(ii) Consider the 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.  ... 
arXiv:math/0610091v1 fatcat:3vad55pyivb47olyuxzcbknzoy

Recent Results on the Algebraic Approach to the CSP [chapter]

Andrei A. Bulatov, Matthew A. Valeriote
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 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.  ... 
doi:10.1007/978-3-540-92800-3_4 fatcat:x56vxo4fobadjmeayv3k35atgi
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