I have a 3-factor experiment, each factor having two levels:

• gt: Genotype: XX vs XY
• sex: Sex: M vs F
• tmt: Treatment: Letrizole (let) vs Vehicle (veh)

I'm interested in the following contrasts:

1. Average main effects of genotype, sex, and treatment across all other levels of other factors
2. Interaction effect of gt:tmt across all levels of sex
3. Interaction effect of sex:tmt across all levels of gt

Then similarly, getting the same information slicing across one or the other level of gt and sex. That is, 

1. Avg main effects of gt and tmt separately in each level of sex (m and f)
2. Avg main effects of sex and tmt separately in each level of gt (xx and xy)
3. Interaction of gt:tmt separately in each level of sex (m and f)
4. Interaction of sex:tmt separately in each level of gt (xx and xy)

Here's what I'm doing.

I have a design matrix that looks like this, and after running the DESeq pipeline, I have 6 contrasts in my results set.

> design(dds)
~gt + tmt + sex + gt:tmt + sex:tmt
> matrix(resultsNames(dds))
     [,1]           
[1,] "Intercept"    
[2,] "gt_xy_vs_xx"  
[3,] "tmt_let_vs_veh"
[4,] "sex_m_vs_f"   
[5,] "gtxy.tmtlet"  
[6,] "tmtlet.sexm"   

And here's what I'm doing to try to get out the main effects. Does this look right?

# average main effects across all levels: get the main effect and half of both contrasts
# for gt xy vs xx
results(dds, contrast=c(0, 1, 0, 0, .5, .5)) 
# for tmt let vs veh
results(dds, contrast=c(0, 0, 1, 0, .5, .5))
# for sex m vs f
results(dds, contrast=c(0, 0, 0, 1, .5, .5))

However, I'm confused about interaction terms. If I want the average gt:tmt interaction across all levels of sex, do I include "half" the interaction of sex:tmt also so I capture this across all levels of sex? Or not? which of these is correct? 

results(dds, contrast=c(0, 0, 0, 0, 1, .5)) 
results(dds, contrast=c(0, 0, 0, 0, 1, 0)) 

And for the second set of results, getting the same information slicing across one or the other level of gt and sex, I'm guessing it'll look something like this?

# main effect of gt xy vs xx in females average across treatment:
# add half the gt:tmt interaction?
results(dds, contrast=c(0, 1, 0, 0, .5, 0))
# main effect of gt xy vs xx in males average across treatment:
# add half the gt:tmt interaction, and all of the tmt:sex(m) interaction?
results(dds, contrast=c(0, 1, 0, 0, .5, 0))
results(dds, contrast=c(0, 1, 0, .5, 1))

I think if I can get these few correct I can handle the rest.

Thanks for any insight!

Yes, I trimmed down the interaction section, because I think it was making people more confused than less. I've now made the vignette section more descriptive and added a picture, and then built up the examples in ?results, although not showing that using numeric contrast you can add half of an interaction, in order to get a sense of an "average" of the effects in both groups. I'll try to add it back in somewhere in this devel cycle.

For your first question, for average genotype effect across the treatments, you would not include a .5 for the "tmtlet.sexm" term. It would just be:

results(dds, contrast=c(0, 1, 0, 0, .5, 0)) 

and similar logic for the others. The reason is that, you do not have a second order interaction here of genotype-treatment-sex, so you assume the genotype-treatment interaction is the same across sex (which is perfectly reasonable, and I think it's always good to try to use only as many terms as you need). So you just need to have the main effect and half of the interaction of genotype with treatment. 

For your second question, this same reasoning applies. You would not add .5 for the "tmtlet.sexm" term but just use:

results(dds, contrast=c(0, 0, 0, 0, 1, 0)) 

or just

results(dds, name="gtxy.tmtlet")

For your third question, the same reasoning tells you that this "average" genotype effect, averaging over treatments, is the same for females and males with this model.