Timeline for How different can the constituents of an Ehrhart quasi-polynomial be?
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| Oct 4, 2020 at 21:26 | comment | added | Sam Hopkins | Note that if we drop the "with 0 diagonal" condition, the answer is known exactly. Namely, the Ehrhart quasi-polynomial then is of the form $P_n(r)+(-1)^rQ_n(r)$ where the degree of $P_n(r)$ is $\binom{n}{2}$ and the degree of $Q_n(r)$ is $\binom{n-1}{2}-1$ if $n$ is odd and $\binom{n-2}{2}-1$ if $n$ is even. See Stanley, "Magic labelings of graphs, symmetric magic squares ..." (doi.org/10.1215/S0012-7094-76-04342-8) and Jia, "Symmetric magic squares and multivariate splines" (doi.org/10.1016/0024-3795(95)00451-3). | |
| May 24, 2018 at 20:30 | history | answered | Brendan McKay | CC BY-SA 4.0 |