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Results tagged with polynomials
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user 33089
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
6
votes
Accepted
How different can the constituents of an Ehrhart quasi-polynomial be?
Let $d=\dim(P)$. First, since $L(t,P)$ is non-decreasing in $t$, for any positive integer $n$ we have
$$f_i((n-1)D+i) \leq f_j((n-1)D+j) \leq f_i(nD+i) \leq f_j(nD+j)$$
whenever $i \leq j$. Thus it …
- 2,743
17
votes
1
answer
495
views
Irreducibility of root-height generating polynomial
The height $ht(\alpha)$ of a positive root $\alpha$ in a (finite, crystallographic) root system $\Phi$ is $\sum_{i=1}^n c_i$ where $\alpha = \sum_{i=1}^n c_i \alpha_i$ is its decomposition as a sum of …
- 2,743