examples of success
The last two days have been really good to me mathematically.
Yesterday I finally found an example verifying my intuition that a certain homomorphism I had constructed wasn't a transfer homomorphism in the most general case.* This had bugged me for the last week as I was writing up my notes from the Granada conference. Though the counterexample is a very specific type and now I wonder if this is the only kind of counterexample there is. It would be pretty neat if that were the case.
Today, I was working on a different factorization theory problem and by accident stumbled upon a four element, half-factorial subset of Z that contains two positive and two negative elements. This had stumped me for months while writing up the strongly taut paper. I had really wanted it for that paper because I felt I could manipulate it into a berzerk example of a half-factorial subset of (Q, +), but eventually I gave up and submitted the paper without any pathological examples. Oh well. Now with this example I have a really strong idea for what such subsets could look like and if Andreas bites the bait, he and I may churn out a paper on this pretty quickly, which would be neat.
*thanks to psifenix for giving me a concrete instance of my counterexample in the algebraic number ring case.
Yesterday I finally found an example verifying my intuition that a certain homomorphism I had constructed wasn't a transfer homomorphism in the most general case.* This had bugged me for the last week as I was writing up my notes from the Granada conference. Though the counterexample is a very specific type and now I wonder if this is the only kind of counterexample there is. It would be pretty neat if that were the case.
Today, I was working on a different factorization theory problem and by accident stumbled upon a four element, half-factorial subset of Z that contains two positive and two negative elements. This had stumped me for months while writing up the strongly taut paper. I had really wanted it for that paper because I felt I could manipulate it into a berzerk example of a half-factorial subset of (Q, +), but eventually I gave up and submitted the paper without any pathological examples. Oh well. Now with this example I have a really strong idea for what such subsets could look like and if Andreas bites the bait, he and I may churn out a paper on this pretty quickly, which would be neat.
*thanks to psifenix for giving me a concrete instance of my counterexample in the algebraic number ring case.