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Dec 11, 2014 at 23:05 comment added Vladimir Dotsenko "Euler characteristic of/for Hilbert series" sounds a bit off to me; I would expect some space or complex to have Euler characteristic, not the Hilbert series. I also only heard the term "graded Euler characteristic" in the knot context. In various disjoint crowds where I saw this thing used, people frequently say "generating function of Euler characteristics" (which effectively means they prefer to change the order of summation in your formula for $\chi$ ;-) ). Another usage I encountered was "Poincare series", implying that "Hilbert" counts dimensions, and "Poincare" - Euler characteristic.
Dec 11, 2014 at 22:20 history edited Ricardo Andrade CC BY-SA 3.0
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Dec 11, 2014 at 22:00 comment added Mariano Suárez-Álvarez Knot theory people use «graded Euler characteristic» if I recall correctly, but it seems restricted to that crowd.
Dec 11, 2014 at 21:53 history asked Mariano Suárez-Álvarez CC BY-SA 3.0