A Generalization of Very Odd Sequences

[摘要] Let $\mathbb N$ be the set of positive integers and $n\in \mathbb N$. Let $\mathbf{a}=(a_0,a_1,\dots, a_{n-1})$ be a sequence of length $n$, with $a_i\in \{0,1\}$. For $0\leq k\leq n-1$, let \[ A_k(\mathbf{a})=\sum_{\substack{0\leq i\leq j\leq n-1\\ j-i=k

[学科分类] 离散数学和组合数学

[关键词] very odd sequence;Pelikan’s conjecture