A PROFINITE APPROACH TO STABLE PAIRS

We give a short proof, using profinite techniques, that idempotent pointlikes, stable pairs and triples are decidable for the pseudovariety of aperiodic monoids. Stable pairs are also described for the pseudovariety of all finite monoids.

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DUALISABILITY OF FINITE SEMIGROUPS

International Journal of Algebra and Computation ◽

10.1142/s0218196703001535 ◽

2003 ◽

Vol 13 (04) ◽

pp. 481-497 ◽

Cited By ~ 7

Author(s):

MARCEL JACKSON

Keyword(s):

Inverse Semigroups ◽

Commutative Monoids ◽

Finite Algebras ◽

Finite Monoids ◽

Finite Semigroups ◽

Entropic Algebra ◽

Aperiodic Monoids

We describe the inherently non-dualisable finite algebras from some semigroup related classes. The classes for which this problem is solved include the variety of bands, the pseudovariety of aperiodic monoids, commutative monoids, and (assuming a reasonable conjecture in the literature) the varieties of all finite monoids and finite inverse semigroups. The first example of an inherently non-dualisable entropic algebra is also presented.

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A note on generalized quasi-contraction

Filomat ◽

10.2298/fil1711091i ◽

2017 ◽

Vol 31 (11) ◽

pp. 3091-3093

Author(s):

Dejan Ilic ◽

Darko Kocev

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Short Proof

In this paper we give a short proof of the main results of Kumam, Dung and Sitthithakerngkiet (P. Kumam, N.V. Dung, K. Sitthithakerngkiet, A Generalization of Ciric Fixed Point Theorems, FILOMAT 29:7 (2015), 1549-1556).

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Short proof that Kneser graphs are Hamiltonian for n ⩾ 4k

Discrete Mathematics ◽

10.1016/j.disc.2021.112430 ◽

2021 ◽

Vol 344 (7) ◽

pp. 112430

Author(s):

Johann Bellmann ◽

Bjarne Schülke

Keyword(s):

Short Proof ◽

Kneser Graphs

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Strongly perfect claw‐free graphs—A short proof

Journal of Graph Theory ◽

10.1002/jgt.22659 ◽

2021 ◽

Author(s):

Maria Chudnovsky ◽

Cemil Dibek

Keyword(s):

Short Proof

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A short note on extreme points of certain polytopes

Special Matrices ◽

10.1515/spma-2020-0005 ◽

2020 ◽

Vol 8 (1) ◽

pp. 36-39

Author(s):

Lei Cao ◽

Ariana Hall ◽

Selcuk Koyuncu

Keyword(s):

Short Proof ◽

Convex Polytopes ◽

Short Note ◽

Convex Polytope ◽

Extreme Points ◽

Alternative Proof ◽

Stochastic Matrices ◽

Doubly Stochastic ◽

Birkhoff's Theorem ◽

Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

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