Timeline for Combinatorics of signed oriented graphs/skew-symmetric matrices
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 16, 2010 at 21:24 | comment | added | Wadim Zudilin | Martin, thank you for the tip. No, I didn't. But I'll try to do so today. | |
| Jun 16, 2010 at 16:08 | comment | added | Martin Rubey | Did you try to interpret the determinant as generating function for non-intersecting lattice paths via Stembridge's theorem (Advances in Mathematics 83, Nonintersecting Paths, Pfaffians, and Plane Partitions)? | |
| Jun 16, 2010 at 14:25 | comment | added | Wadim Zudilin | Victor and Robin, thanks for notifying this mistake. Yes, of course, I meant that only the squares have to be taken in the range. | |
| Jun 16, 2010 at 14:18 | comment | added | Victor Protsak | Wadim, Robin was commenting on your statement that "det(V) seems to assume all possible odd positive values restricted only by Hadamard's_inequality": there is an additional requirement that det(V) be a perfect square (or you should say Pfaffian). | |
| Jun 16, 2010 at 9:09 | comment | added | Wadim Zudilin | Robin, I provide the required links which explain that $\det(V)$ is the square of the Pfaffian. I can even compute the Pfaffian as a single determinant of a $(n/2)\times(n/2)$ matrix in the case $v_{ij}=\epsilon_{i-j}$. A tournament is another way to say a complete signed (oriented) graph, but I am looking for a structure of graphs satisfying $\det(V)=1$. | |
| Jun 16, 2010 at 8:28 | comment | added | Robin Chapman | This combinatorial structure (a complete graph with an orientation) is known as a tournament. Also, as a skew-symmetric matrix, $\det(V)$ is a square (the square of the Pfaffian of $V$). | |
| Jun 16, 2010 at 8:08 | history | asked | Wadim Zudilin | CC BY-SA 2.5 |