Combinatorial structures in loops
نویسندگان
چکیده
منابع مشابه
Combinatorial Structures in Loops
A Steiner triple system (STS) of order n, J,, = [S, 5a], is an arrangement of the elements of an n-set S into a set 5 ~ of triples such that every pair of elements in S occur together in exactly one triple of ~ A necessary and sufficient condition that an STS of order n exist is that n--1, 3 (mod 6). An STS J,, which has a group of automorphisms G which is regular (sharply transitive) on the el...
متن کاملCombinatorial Structures in Loops I. Elements of the Decomposition Theory
Difference sets have been extensively studied in groups, principally in Abelian groups. Here we extend the notion of a difference set to loops. This entails considering the class of principal block partial designs (PBPDs) and (v, k, A) designs. By means of a certain permutation matrix decomposition of the incidence matrices of a system and...
متن کاملCombinatorial Aspects of Code Loops
The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T.Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E....
متن کاملRegeneration in random combinatorial structures
Theory of Kingman’s partition structures has two culminating points • the general paintbox representation, relating finite partitions to hypothetical infinite populations via a natural sampling procedure, • a central example of the theory: the Ewens-Pitman two-parameter partitions. In these notes we further develop the theory by • passing to structures enriched by the order on the collection of...
متن کاملCombinatorial Structures in Nonlinear Programming
Non-smoothness and non-convexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g. through the use of ”max”, ”min”, or ”if” statements in a model, or implicit as in the case of bilevel optimization where the combinatorial structure arises from the possible choices of active constraints in th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 1974
ISSN: 0025-5874,1432-1823
DOI: 10.1007/bf01221880