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China has committed to ambitious targets to reduce its carbon emissions in the next decades, in order to combat climate change and improve the environment. The realization of the targets depends on the fair and effective mitigation plans of all provinces. However, with varying ecological and environmental conditions and social-economic development, it is a critical issue to quantify the provinces' efforts equally. This paper proposed a comprehensive fE index in coordinating ecology, equity and economy, by accounting for carbon emissions and sinks to characterize provincial carbon emission status in China, from 2000 to 2017, which shows a spatial pattern of "boundary high, central low". The provinces with higher fE value (>1.5) in boundary areas can be seen as "relative equality" provinces with good ecology circulation, equity and economic efficiency. The provinces with lower fE value (<0.7) in central areas around Bohai Bay are regarded as "severe inequality" provinces, and are identified as the hot-spot provinces, which have emitted more CO2 than their equity share by occupying the carbon emission space of other provinces in recent decades. These results could provide a reference for a provincial guide for carbon reduction and sustainable development of the low-carbon economy. [ABSTRACT FROM AUTHOR]