n-Permutability is not join-prime for n ≥ 5

Equations implying congruence n-permutability and semidistributivity

T. Dent, K. Kearnes and Á. Szendrei have defined the derivative, Σ′, of a set of equations Σ and shown, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutability for some n, and for congruence semidistributivity.

NOTES ON CONGRUENCE n-PERMUTABILITY AND SEMIDISTRIBUTIVITY

In [1] T. Dent, K. Kearnes and Á. Szendrei define the derivative, Σ′, of a set of equations Σ and show, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutable for some n, and for congruence semidistributivity. In a recent paper [1] T. Dent, K. Kearne...

The Burau representation is not faithful for n = 5

The Burau representation is a natural action of the braid group Bn on the free Z[t; t−1]{module of rank n−1. It is a longstanding open problem to determine for which values of n this representation is faithful. It is known to be faithful for n = 3. Moody has shown that it is not faithful for n 9 and Long and Paton improved on Moody’s techniques to bring this down to n 6. Their construction uses...

The Burau Representation is Not Faithful for n = 5 Stephen

Diag-Join: An Opportunistic Join Algorithm for 1:N Relationships

Time of creation is one of the predominant (often implicit) clustering strategies found not only in Data Warehouse systems: line items are created together with their corresponding order, objects are created together with their subparts and so on. The newly created data is then appended to the existing data. We present a new join algorithm, called DiagJoin, which exploits time-of-creation clust...