共查询到20条相似文献,搜索用时 15 毫秒
1.
Communicated by J.M. Howie 相似文献
2.
Michael Gass 《Semigroup Forum》1989,39(1):335-345
In this article a method is given for embedding a finitely generated free monoid as a dense subset of the unit interval. This
gives an order topology for the monoid such that the submonoids generated by an important class of maximal codes occur as
“thick” subsets.
As an ordered topological space, the notion of thickness in a frec monoid can be interpreted in a number of ways. One such
notion is that of density. In particular, subsets of a free monoid that fail to meet all two sided ideals (the thin sets,
of which recognizable codes are an example) are shown (corollary 4.2) to be nowhere dense. Furthermore, it is shown (corollary
5.1) that a thin code is maximal if and only if the submonoid that it generates is dense on some interval. Thus thin codes
that are maximal are precisely those that generate thick submonoids.
Another notion of thickness is that of category. The embedding allows the free monoid to be viewed as a subspace of the unit
interval. In theorem 5.6 it is shown that a thin code is maximal just in case the closure of the submonoid that it generates
is second category in the unit interval. A mild connection with Lebesque measure is then made.
In what follows, all free monoids are assumed to be generated by a finite set of at least two elements. IfA is such a set, thenA
* denotes the free monoid generated byA. The setA is called an alphabet, the elements ofA
* are called words, ande denotes the empty word inA
*. Topological terminology and notation follows that of Kelley [2]. 相似文献
3.
Toby Kenney 《Journal of Algebraic Combinatorics》2014,39(3):719-731
Associated with any Coxeter group is a Coxeter monoid, which has the same elements, and the same identity, but a different multiplication. (Some authors call these Coxeter monoids 0-Hecke monoids, because of their relation to the 0-Hecke algebras—the q=0 case of the Hecke algebra of a Coxeter group.) A Coxeter group is defined as a group having a particular presentation, but a pair of isomorphic groups could be obtained via non-isomorphic presentations of this form. We show that when we have both the group and the monoid structure, we can reconstruct the presentation uniquely up to isomorphism and present a characterisation of those finite group and monoid structures that occur as a Coxeter group and its corresponding Coxeter monoid. The Coxeter monoid structure is related to this Bruhat order. More precisely, multiplication in the Coxeter monoid corresponds to element-wise multiplication of principal downsets in the Bruhat order. Using this property and our characterisation of Coxeter groups among structures with a group and monoid operation, we derive a classification of Coxeter groups among all groups admitting a partial order. 相似文献
4.
程辉 《纯粹数学与应用数学》2001,17(3):197-200,213
讨论了图的广义字典序积的自同态幺半群的性质,给出了广义字典序积图X[Yz|x∈V(X)]的自同态幺半群与X,Yx(x∈V(X))的自同态幺半群的圈积相等的充要条件。 相似文献
5.
In this paper we determine the \(G\times G\) orbits of both an even orthogonal monoid and an even special orthogonal monoid, where G is the unit group of the even special orthogonal monoid. We then use the orbit decompositions to compute the orders of these monoids over a finite field. 相似文献
6.
《Applied Mathematics Letters》2006,19(10):1037-1041
At INDOCRYPT 2003 Abisha, Thomas, and Subramanian proposed two public key schemes based on word problems in free partially commutative monoids and groups. We show that both proposals are vulnerable to chosen ciphertext attacks, and thus in the present form must be considered as insecure. 相似文献
7.
A function on an algebra is congruence preserving if for any congruence, it maps congruent elements to congruent elements. We show that on a free monoid generated by at least three letters, a function from the free monoid into itself is congruence preserving if and only if it is of the form \({x \mapsto w_{0}xw_{1} \cdots w_{n-1}xw_n }\) for some finite sequence of words \({w_0,\ldots ,w_n}\). We generalize this result to functions of arbitrary arity. This shows that a free monoid with at least three generators is a (noncommutative) affine complete algebra. As far as we know, it is the first (nontrivial) case of a noncommutative affine complete algebra. 相似文献
8.
Aldo de Luca 《Proceedings of the Steklov Institute of Mathematics》2011,274(1):124-135
This paper is a survey of several results of combinatorial nature which have been obtained starting from a palindromization
map on a free monoid A* introduced by the author in 1997 in the case of a binary alphabet and, successively, generalized by other authors for arbitrary
finite alphabets. If one extends the action of the palindromization map to infinite words, one can generate the class of all
standard episturmian words, which includes standard Sturmian words and Arnoux-Rauzy words. In this framework, an essential
role is played by the class of palindromic prefixes of all standard episturmian words called epicentral words. These words
are precisely the images of A* under the palindromization map. Epicentral words have several different representations and satisfy interesting combinatorial
properties. A further extension of the palindromization map to a t9-palindromization map, where t9 is an arbitrary involutory antimorphism of A*, is also briefly discussed. 相似文献
9.
10.
A group G of units in a monoid S is called left normal if sG ⊆ Gs for all s ε S. The centralizer Z of G in S is the set of
all s ε S with sg=gs for all g ε G. Always l ε Z, and if S has a zero 0, then 0 ε Z. We show that in a compact connected monoid
S with zero the centralizer Z of any left normal (closed) group G of units is connected.
This work was supported by NSF. 相似文献
11.
Cristian Calude 《Discrete Mathematics》1976,15(4):307-310
A complete solution is given of the problem of S. Marcus concerning the construction of a “better” distance in the free monoids from the viewpoint of measuring the difference of contextual behaviour with respect to a given language. 相似文献
12.
Communicated by J.M. Howie 相似文献
13.
14.
《Discrete Applied Mathematics》1986,14(1):105-108
In this paper we evaluate the complexity of an algorithm for deciding whether a partially commutative free monoid has an infinite number of square-free elements. 相似文献
15.
16.
17.
研究了幺半群半直积上的同余,给出了幺半群半直积的所谓同余分解定理,并特别讨论了幺半群左正则纯整半直积及其子类上的同余. 相似文献
18.
19.
20.
Shripad M. Garge 《Proceedings Mathematical Sciences》2005,115(4):411-427
The aim of this paper is to investigate the order coincidences among the finite semisimple groups and to give a reasoning
of such order coincidences through the transitive actions of compact Lie groups.
It is a theorem of Artin and Tits that a finite simple group is determined by its order, with the exception of the groups
(A3(2), A2(4)) and(B
n
(q), C
n
(q)) forn ≥ 3,q odd. We investigate the situation for finite semisimple groups of Lie type. It turns out that the order of the finite
group H(
) for a split semisimple algebraic groupH defined over
, does not determine the groupH up to isomorphism, but it determines the field
under some mild conditions. We then put a group structure on the pairs(H
1,H
2) of split semisimple groups defined over a fixed field
such that the orders of the finite groups H1(
) and H2(
) are the same and the groupsH
i
have no common simple direct factors. We obtain an explicit set of generators for this abelian, torsion-free group. We finally
show that the order coincidences for some of these generators can be understood by the inclusions of transitive actions of
compact Lie groups. 相似文献