Auxins have a minor role in the initiation of flowering and development of reproductive organs, but don't actually change the sex of plants. Their main role is to promote stem elongation and inhibit growth of lateral buds :)
Auxins and ethylene have long been known to enhance femaleness in a number of species, e. g., hemp, various cucurbits and corn, to name a few, while gibberellins tend to enhance maleness. There is a long history of publications on the topic of sex expression in plants, many of which involve changing sex of flowers with hormone applications. High levels of auxin induce the production of ethylene, which often explains a number of phenomena, including abscission and epinasty. What exact role auxin may play at the molecular level in regulation of sex expression may or may not be known, as I haven't kept up with recent research in this area. However, I disagree with Pegman that the main role of auxins is stem elongation and inhibition of lateral buds, which is generally caused by ethylene (that may be induced by high levels of auxin). At the molecular level, movement of auxin throughout the plant via various carriers is critical in many aspects of plant development and growth. A recent text on plant physiology by Taiz and Zeiger will give you a good introduction and update on recent research.
I do agree with Gregg's points.Ethylene is mainly responsible for sex expression which is produced during high auxin activity.It increases femaleness.Another hormone results in maleness.
I do also agree Gregg's explanation about the effects of auxin on ethylene production and then change in sex expression as a result. Auxin has several effects on plant growth and development and there is a cross-talk between auxin and ethylene. However, we need to know what type and concentration of auxin and time of application in order to get what we want. The synthetic auxin 2,4-D could be herbicidal at higher concentrations causing epinasty, abscission and death of plants or their parts, by increasing ethylene production. While at uM concentrations it could delay abscission and senescence by antagonizing the effects of ethylene.
And to clear up another point, what causes stem elongation varies according to a number of factors. Gibberellins are responsible for stem elongation in a number of cases, for example in peas, in which certain genotypes are responsible for the amount of growth in height that takes place. On the other hand, in stem bending, it's elongation of individual cells by auxin that is involved. Turning off ethylene production can result in stem elongation in emerging seedlings. And so on. None of this is simple. Most plant growth phenomenona are orchestrated by interactions of many growth factors (with much cross-talk) and these factors are influenced by genetics and environment.
And here's an interesting fairly recent paper: Wang et al. 2010 Ethylene perception is involved in female cucumber flower development. The Plant Journal 61:862-872. doi: 10.1111/j.1365-313X.2009.04114.x
Here are more recent article that explain the details:
1. Involvement of Ethylene Biosynthesis and Signalling in the Transition from Male to Female Flowering in the Monoecious Cucurbita pepo. J Plant Growth Regul. December 2013, Volume 32, Issue 4, pp 789–798. DOI 10.1007/s00344-013-9344-6
2. Transcriptomic Analysis Implies That GA Regulates Sex Expression via Ethylene-Dependent and Ethylene-Independent Pathways in Cucumber (Cucumis sativus L.)