bio | website | imar.ro/~mbuliga |
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location | ||
age | ||
visits | member for | 3 years, 9 months |
seen | Apr 24 '13 at 9:58 | |
stats | profile views | 1,821 |
Jun 25 |
awarded | Yearling |
Apr 24 |
answered | Oriented Reidemeister move R2d by splices and loop adding/erasing? |
Apr 24 |
comment |
Oriented Reidemeister move R2d by splices and loop adding/erasing?
Correction: "This would mean that the order of applications of splices 1/2 and loop 1/2" ... is commutative. |
Apr 24 |
comment |
Oriented Reidemeister move R2d by splices and loop adding/erasing?
Thanks, I'll try. But is not obvious that the spliced form is invariant. This would mean that the order of applications of splices 1/2 and loop 1/2. Notice that all moves go in both directions and one may obtain complex diagrams from simple ones. In case anybody interested, what is not clear at all to me is what happens if we work not with tangle diagrams, which are globally planar graphs, but with "locally planar" tangle diagrams, i.e. we allow the possibility that two edges of the diagram cross without counting this a real crossing. |
Apr 23 |
asked | Oriented Reidemeister move R2d by splices and loop adding/erasing? |
Oct 4 |
comment |
When a semigroup extension $S \times A$ of a semigroup $S$ with a commutative group $A$ contains a copy of $S$?
No, I've seen both names used for both objects, it's like $\mathbb{N}$, which contains or not $0$, according to pedagogical school of thought. |
Oct 2 |
comment |
When a semigroup extension $S \times A$ of a semigroup $S$ with a commutative group $A$ contains a copy of $S$?
Thank you, I have not realized that trivially the example 2 is a direct product. |
Oct 2 |
accepted | When a semigroup extension $S \times A$ of a semigroup $S$ with a commutative group $A$ contains a copy of $S$? |
Oct 2 |
comment |
When a semigroup extension $S \times A$ of a semigroup $S$ with a commutative group $A$ contains a copy of $S$?
Thanks for comment, I replaced "semidirect product" with "semigroup extension". |
Oct 2 |
revised |
When a semigroup extension $S \times A$ of a semigroup $S$ with a commutative group $A$ contains a copy of $S$?
changed "semidirect product" with "semigroup extension" |
Oct 2 |
asked | When a semigroup extension $S \times A$ of a semigroup $S$ with a commutative group $A$ contains a copy of $S$? |
Sep 20 |
comment |
Computational complexity of multiplication in a nilpotent group?
Thanks! Interesting that transformations of $A$ and $B$ into $3n \times 3n$ matrices are different! |
Sep 19 |
comment |
Computational complexity of multiplication in a nilpotent group?
Dear Henry, after more thinking, I don't believe that "you can reduce n×n matrix multiplication to the 3n×3n upper triangular case. (Use nine n×n blocks, with identity matrices on the diagonal and a zero matrix in the upper right corner.)" There is something wrong there, are you saying that there is an injective morphism from $GL(n)$ to the group of $3n \times 3n$ upper triangular matrices? |
Sep 17 |
awarded | Commentator |
Sep 15 |
comment |
Computational complexity of multiplication in a nilpotent group?
You are right, I was hoping I missed something, that already for the Heisenberg group there is a difference. |
Sep 14 |
comment |
Computational complexity of multiplication in a nilpotent group?
Actually, if anybody cares, here is explained the motivation for the question: chorasimilarity.wordpress.com/2012/09/14/… |
Sep 14 |
comment |
Computational complexity of multiplication in a nilpotent group?
Thank you for the answer. What about the Heisenberg group $H(n) = R^{n} \times R^{n} \times R$? It has $m=2$. |
Sep 13 |
comment |
How fast can we *really* multiply matrices?
Dear Henry, I asked a somehow related question, see mathoverflow.net/questions/106899/… |
Sep 12 |
revised |
Computational complexity of multiplication in a nilpotent group?
added 1651 characters in body |
Sep 11 |
comment |
Computational complexity of multiplication in a nilpotent group?
Thanks for all questions! First, any type of estimate would do, provided that it gives a kind of interpolation between the addition (the commutative case, $m=1$) and pure matrix multiplication (like in example 3). Btw, I suspect that even in the case of example 3, there should be a much better estimate than $N^{3}$ for multiplication of upper triangular matrices. Secondly, in case of Carnot groups it is customary to take exponential equate to identity, or otherwise just use the Baker-Campbell-Hausdorff formula (which is a finite sum because of the nilpotency). |