1. Reminder on quotient groups Let G be a group and H a subgroup of G. We have seen that the left cosets xH of H in G give a partition of G. Motivated by the case of quotients of rings by ideals, it is natural to consider the product operation on cosets. Recall that for any subsets S, T of G, by ST we mean {st | s ∈ S, t ∈ T }. If G is commutative, the product of two left cosets is another left...

1 13 4. Free rational curves 14 5. Uniruledness 16 5.1. Definitions equivalent to uniruledness 16 5.2. Examples and consequences of uniruledness 18 6. Rational connectivity 20 6.1. Definitions equivalent to rational connectivity 21 6.2. Rational chain-connectivity implies rational connectivity 22 6.3. Examples and consequences of rational connectivity 26 7. The MRC quotient 27 7.1. Quotients by...

A nilmanifold is a (left) quotient of nilpotent Lie group by cocompact lattice. hypercomplex structure on manifold triple complex operators satisfying the quaternionic relations. compact equipped with left-invariant structure. Such admits whole 2-dimensional sphere $S^2$ structures induced quaternions. We prove that for any $M$ and generic $L\in S^2$, $(M,L)$ has algebraic dimension 0. stronger...

We propose linear systems of hedge language equations (LSH) as a formalism to represent regular hedge languages. These linear systems are suitable for several computations in the algebra of regular hedge languages. We indicate algorithms to translate between representations by hedge automata and LSH, and for the computation of LSH for the intersection, quotient, left and right factors of regula...

We introduce an excedance statistic for the group of affine permutations S̃n and determine the generating function of its distribution. The proof involves working with enumerating lattice points in a skew version of the root polytope of type A. We also show that the left coset representatives of the quotient S̃n/Sn correspond to increasing juggling sequences and determine their Poincaré series.

An efficient parallel adder under left-to-right input arrival is proposed. Making full use of the delay of the input arrival, it produces the sum within a small constant delay after the arrival of the final bits. Its amount of hardware is proportional to the operand length. It can be applied to the quotient conversion in an array divider.

Abstract In this paper, we classify the compact locally homogeneous non-gradient m -quasi Einstein 3- manifolds. Along way, also prove that given a quotient of Lie group any dimension is Einstein, potential vector field X must be left invariant and Killing. We nontrivial metrics are product two metrics. show S 1 only manifold which admits metric nontrivially Einstein.

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P, induced from those for seven points on P. The seven point ball quotient example DM(2, 1) does not appear on Mostow’s original list [9], but does appear on Thurston’s corrected version [12]. We show that DM(2, 1) is a finite cover of the moduli space of cubic surfaces MC en...