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 \[ A_k(\mathbf{a})=\sum_{\substack{0\leq i\leq j\leq n-1\\ j-i=k}} a_ia_j.\] The sequence $\mathbf{a}$ is called a very odd sequence if $A_k(\mathbf{a})$ is odd for all $0\leq k\leq n-1$. In this paper, we study a generalization of very odd sequences and give a characterisation of these sequences.
@article{10_37236_5075,
author = {Cheng Yeaw Ku and Kok Bin Wong},
title = {A generalization of very odd sequences},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/5075},
zbl = {1311.11017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5075/}
}
TY - JOUR
AU - Cheng Yeaw Ku
AU - Kok Bin Wong
TI - A generalization of very odd sequences
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5075/
DO - 10.37236/5075
ID - 10_37236_5075
ER -
%0 Journal Article
%A Cheng Yeaw Ku
%A Kok Bin Wong
%T A generalization of very odd sequences
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5075/
%R 10.37236/5075
%F 10_37236_5075
Cheng Yeaw Ku; Kok Bin Wong. A generalization of very odd sequences. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/5075
