Timeline for Almost orthogonal maps $f:\omega \to \{-1,1\}$

9 events

when toggle format	what		by	license	comment
Sep 4 at 14:54	history	edited	Christopher King	CC BY-SA 4.0	added 35 characters in body
Aug 31 at 10:43	comment	added	Claude Chaunier		Might I suggest $$\begin{align}\prod_{j=0}^{k} \left((-1)^{0(\lambda_j+\mu_j)}+(-1)^{1(\lambda_j+\mu_j})\right) = \sum_{(b_j)\in\{0,1\}^{k+1}}\prod_{j=0}^{k} (-1)^{b_j(\lambda_j+\mu_j)}\\ = \sum_{(b_j)\in\{0,1\}^{k+1}}(-1)^{\sum_{j=0}^{k}b_j(\lambda_j+\mu_j)}\\ = \sum_{r=0}^{2^{k+1}-1}(-1)^{\sum_{j=0}^{k}b_j(r)\lambda_j}(-1)^{\sum_{j=0}^{k}b_j(r)\mu_j}\;?\end{align}$$
Aug 31 at 10:00	vote	accept	Dominic van der Zypen
Aug 30 at 18:17	comment	added	Christopher King		Might I suggest including the proof of $$\prod_{j=0}^{k} (1+(-1)^{\lambda_j \mu_j}) = \sum_{r=0}^{2^{k+1}-1} \chi_{\lambda}(r) \chi_{\mu}(r)$$. It is a lot of mental steps!
Aug 30 at 18:01	comment	added	David E Speyer		@TarasBanakh Oops! That's the trouble with thinking multiplicatively and writing additively. Fixed now.
Aug 30 at 18:01	history	edited	David E Speyer	CC BY-SA 4.0	edited body
Aug 30 at 17:50	comment	added	Taras Banakh		@DavidESpeyer Maybe $b_k(n)$ is equal to $0$ (not to $1$) for all but finitely many $k$?
Aug 30 at 17:27	history	edited	David E Speyer	CC BY-SA 4.0	added 58 characters in body
Aug 30 at 16:49	history	answered	David E Speyer	CC BY-SA 4.0