Timeline for Hermite normal form in families
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2009 at 17:53 | vote | accept | Danny Calegari | ||
| Nov 27, 2009 at 6:44 | answer | added | Greg Kuperberg | timeline score: 3 | |
| Nov 21, 2009 at 7:22 | comment | added | Danny Calegari | Unfortunately, I don't think it is that simple. For example, a family of 2x2 upper triangular matrices with 2s on the diagonal and x in the upper right has "periodic" Hermite normal form over Z (the upper right entry alternates between 0 and 1). This is why I speculated about Ehrhart theory (eg. maybe the entries are eventually quasipolynomials) but this is just a guess too. I do think your guess is probably true for some "generic" families, in a sense that needs a bit more clarification . . . | |
| Nov 21, 2009 at 3:46 | comment | added | Qiaochu Yuan | My guess is that for x sufficiently large the Hermite normal form itself consists of integral polynomials. One should be able to prove this by computing the analogue of the Hermite normal form over Z[x] and then showing that it satisfies the conditions of the the usual Hermite normal form for large x. | |
| Nov 21, 2009 at 3:06 | history | asked | Danny Calegari | CC BY-SA 2.5 |