Let p(x_1,...,x_n) =\sum_{ (r_1,...,r_n) \in I_{n,n} } a_{(r_1,...,r_n) } \prod_{1 \leq i \leq n} x_{i}^{r_{i}}
be homogeneous polynomial of degree n in n real variables with integer nonnegative coefficients.
The support of such polynomial p(x_1,...,x_n)
is defined as $supp(p) = \{(r_1,...,r_n) \in I_{n,n} : a_{(r_1,...,r_n)} \neq 0 ... more >>>

Let \mathcal{M} be a bridgeless matroid on ground set \{1,\ldots, n\} and f_{\mathcal{M}}: \{0,1\}^n \to \{0, 1\} be the indicator function of its independent sets. A folklore fact is that f_\mathcal{M} is ``evasive," i.e., D(f_\mathcal{M}) = n where D(f) denotes the deterministic decision tree complexity of f. Here we prove ... more >>>