Results 1  10
of
348
SOME GENERAL PROPERTIES OF LAD AND
"... Abstract. A groupoid that satisfies the left invertive law: ab·c = cb · a is called an AGgroupoid. We extend the concept of left abelian distributive groupoid (LAD) and right abelian distributive groupoid (RAD) to introduce new subclasses of AGgroupoid, left abelian distributive AGgroupoid and r ..."
Abstract
 Add to MetaCart
and right abelian distributive AGgroupoid. We give their enumeration up to order 6 and find some basic relations of these new classes with other known subclasses of AGgroupoids and other relevant algebraic structures. We establish a method to test an arbitrary AGgroupoid for these classes. 1.
1 Centro de Álgebra, Universidade de Lisboa,
"... Abstract. Enumeration and classification of mathematical entities is an important part of mathematical research in particular in finite algebra. For algebraic structures that are more general than groups this task is often only feasible by use of computers due to the sheer number of structures that ..."
Abstract
 Add to MetaCart
that have to be considered. In this paper we present the enumeration and partial classification of AGgroupoids — groupoids in which the identity (ab)c = (cb)a holds — of up to order 6. The results are obtained with the help of the computer algebra system GAP and the constraint solver Minion by making use
Enumerating AGGroups with a Study of Smaradache AGGroups
"... AGgroups are a generalisation of Abelian groups. They correspond to groupoids with a left identity, unique inverses, and satisfy the identity (xy)z = (zy)x. We present the first enumeration result for AGgroups up to order 11 and give a lower bound for order 12. The counting is performed with the f ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
AGgroups are a generalisation of Abelian groups. They correspond to groupoids with a left identity, unique inverses, and satisfy the identity (xy)z = (zy)x. We present the first enumeration result for AGgroups up to order 11 and give a lower bound for order 12. The counting is performed
Isomorphism conjectures in algebraic Ktheory
 J. Amer. Math. Soc
, 1993
"... 1.1 The Isomorphism Conjecture in algebraic Ktheory........ 2 1.2 Main Results and Corollaries.................... 4 1.3 A brief outline............................ 6 ..."
Abstract

Cited by 165 (13 self)
 Add to MetaCart
1.1 The Isomorphism Conjecture in algebraic Ktheory........ 2 1.2 Main Results and Corollaries.................... 4 1.3 A brief outline............................ 6
Enumeration of unrooted maps of a given genus
 JOURNAL OF COMBINATORIAL THEORY, SERIES B 96 (2006) 706–729
, 2006
"... Let Ng(f) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(f) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2, 3 (Bender and Canfield, 1991). In the present paper we derive an enumeration formula for the number Θγ (e) of unrooted maps on an orientable ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Let Ng(f) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(f) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2, 3 (Bender and Canfield, 1991). In the present paper we derive an enumeration formula for the number Θγ (e) of unrooted maps
Modular Operads
 COMPOSITIO MATH
, 1994
"... We develop a "higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the definition. We study a functor F on the category of modular operads, the Feynman transform, which generalizes Kontsevich's graph complexes and also the bar constructi ..."
Abstract

Cited by 103 (5 self)
 Add to MetaCart
We develop a "higher genus" analogue of operads, which we call modular operads, in which graphs replace trees in the definition. We study a functor F on the category of modular operads, the Feynman transform, which generalizes Kontsevich's graph complexes and also the bar construction for operads. We calculate the Euler characteristic of the Feynman transform, using the theory of symmetric functions: our formula is modelled on Wick's theorem. We give applications to the theory of moduli spaces of pointed algebraic curves.
Fuzzy AGSubgroups
"... Abstract. An AGgroup is a generalization of an abelian group. A groupoid (G, ·) is called an AGgroup, if it satisfies the identity (ab)c = (cb)a, called the left invertive law, contains a unique left identity and inverse of its every element. We extend the concept of AGgroup to fuzzy AGgroup. We ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Abstract. An AGgroup is a generalization of an abelian group. A groupoid (G, ·) is called an AGgroup, if it satisfies the identity (ab)c = (cb)a, called the left invertive law, contains a unique left identity and inverse of its every element. We extend the concept of AGgroup to fuzzy AG
Results 1  10
of
348