Canonical bijection betweenD of (0, 1)-matrix semigroupsof (0, 1)-matrix semigroups

1973 ◽  
Vol 4 (4) ◽  
pp. 303-305 ◽  
Author(s):  
Kim Ki-Hang Butler
Keyword(s):  
Canonical Bijection ◽  
Matrix Semigroups

A Perron-Frobenius-type Theorem for Positive Matrix Semigroups

Positivity ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 61-72
Author(s):  
L. Livshits ◽  
G. MacDonald ◽  
H. Radjavi
Keyword(s):  
Type Theorem ◽  
Positive Matrix ◽  
Matrix Semigroups

scholarly journals Complex representations of matrix semigroups

1991 ◽  
Vol 323 (2) ◽  
pp. 563-581 ◽  
Author(s):  
Jan Okniński ◽  
Mohan S. Putcha
Keyword(s):  
Matrix Semigroups

scholarly journals Symmetric Chain Decompositions of Products of Posets with Long Chains

10.37236/7124 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Stefan David ◽  
Hunter Spink ◽  
Marius Tiba
Keyword(s):  
Minimal Element ◽  
Difficult Case ◽  
Chain Decomposition ◽  
Graded Poset ◽  
Canonical Bijection ◽  
Symmetric Chain Decomposition ◽  
Symmetric Chain ◽  
Long Chains

We ask if there exists a symmetric chain decomposition of the cuboid $Q_k \times n$ such that no chain is taut, i.e. no chain has a subchain of the form $(a_1,\ldots, a_k,0)\prec \cdots\prec (a_1,\ldots,a_k,n-1)$. In this paper, we show this is true precisely when $k \ge 5$ and $n\ge 3$. This question arises naturally when considering products of symmetric chain decompositions which induce orthogonal chain decompositions — the existence of the decompositions provided in this paper unexpectedly resolves the most difficult case of previous work by the second author on almost orthogonal symmetric chain decompositions (2017), making progress on a conjecture of Shearer and Kleitman (1979). In general, we show that for a finite graded poset $P$, there exists a canonical bijection between symmetric chain decompositions of $P \times m$ and $P \times n$ for $m, n\ge rk(P) + 1$, that preserves the existence of taut chains. If $P$ has a unique maximal and minimal element, then we also produce a canonical $(rk(P) +1)$ to $1$ surjection from symmetric chain decompositions of $P \times (rk(P) + 1)$ to symmetric chain decompositions of $P \times rk(P)$ which sends decompositions with taut chains to decompositions with taut chains.

Complex Representations of Matrix Semigroups

1991 ◽  
Vol 323 (2) ◽  
pp. 563 ◽  
Author(s):  
Jan Okninski ◽  
Mohan S. Putcha
Keyword(s):  
Matrix Semigroups

Group relationships and homomorphisms of Boolean matrix semigroups

1984 ◽  
Vol 28 (4) ◽  
pp. 448-452 ◽  
Author(s):  
K.H. Kim ◽  
F.W. Roush
Keyword(s):  
Boolean Matrix ◽  
Group Relationships ◽  
Matrix Semigroups

The Quasi-Isomorphism Theorem

2019 ◽  
pp. 185-194
Author(s):  
Richard Evan Schwartz
Keyword(s):  
Affine Transformation ◽  
Equivalence Theorem ◽  
Isomorphism Theorem ◽  
Orbit Equivalence ◽  
Geometric Properties ◽  
Projection Theorem ◽  
Canonical Bijection ◽  
Arithmetic Graph

This chapter proves the Quasi-Isomorphism Theorem modulo two technical lemmas, which will be dealt with in the next two chapters. Section 18.2 introduces the affine transformation TA from the Quasi-Isomorphism Theorem. Section 18.3 defines the graph grid GA = TA(Z2) and states the Grid Geometry Lemma, a result about the basic geometric properties of GA. Section 18.4 introduces the set Z* that appears in the Renormalization Theorem and states the main result about it, the Intertwining Lemma. Section 18.5 explains how the Orbit Equivalence Theorem sets up a canonical bijection between the nontrivial orbits of the plaid PET and the orbits of the graph PET. Section 18.6 reinterprets the orbit correspondence in terms of the plaid polygons and the arithmetic graph polygons. Everything is then put together to complete the proof of the Quasi-Isomorphism Theorem. Section 18.7 deduces the Projection Theorem (Theorem 0.2) from the Quasi-Isomorphism Theorem.

scholarly journals On bisimple semigroups generated by a finite number of idempotents

1982 ◽  
Vol 33 (1) ◽  
pp. 92-101 ◽  
Author(s):  
Karl Byleen
Keyword(s):  
Finite Number ◽  
Partial Order ◽  
Natural Partial Order ◽  
Rees Matrix Semigroups ◽  
Matrix Semigroups ◽  
Completely Simple

AbstractNon-completely simple bisimple semigroups S which are generated by a finite number of idempotents are studied by means of Rees matrix semigroups over local submonoids eSe, e = e2 ∈ S. If under the natural partial order on the set Es of idempotents of such a semigroup S the sets ω(e) = {ƒ ∈ Es: ƒ ≤ e} for each e ∈ Es are well-ordered, then S is shown to contain a subsemigroup isomorphic to Sp4, the fundamental four-spiral semigroup. A non-completely simple hisimple semigroup is constructed which is generated by 5 idempotents but which does not contain a subsemigroup isomorphic to Sp4.

scholarly journals Generators and relations of Rees matrix semigroups

1999 ◽  
Vol 42 (3) ◽  
pp. 481-495 ◽  
Author(s):  
H. Ayik ◽  
N. Ruškuc
Keyword(s):  
Rees Matrix Semigroup ◽  
Finitely Generated ◽  
Finite Generation ◽  
Generators And Relations ◽  
Rees Matrix Semigroups ◽  
Finite Presentability ◽  
Matrix Semigroup ◽  
Finitely Presented ◽  
Matrix Semigroups ◽  
The Ideal

In this paper we consider finite generation and finite presentability of Rees matrix semigroups (with or without zero) over arbitrary semigroups. The main result states that a Rees matrix semigroup M[S; I, J; P] is finitely generated (respectively, finitely presented) if and only if S is finitely generated (respectively, finitely presented), and the sets I, J and S\U are finite, where U is the ideal of S generated by the entries of P.

Certain rees matrix semigroups with universal properties

1981 ◽  
Vol 22 (1) ◽  
pp. 101-118 ◽  
Author(s):  
Mario Petrich ◽  
Norman R. Reilly
Keyword(s):  
Rees Matrix Semigroups ◽  
Universal Properties ◽  
Matrix Semigroups
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