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COUNTING THE FACES OF RANDOMLY-PROJECTED HYPERCUBES AND ORTHANTS, WITH APPLICATIONS
RANDOMLY-PROJECTED ORTHANTS
2015/8/21
Let RN
+ denote the positive orthant; the expected number of k-faces of
the random cone ARN
+ obeys Efk(ARN
+)/fk(RN
+) = 1 − PN−n,N−k. The
formula applies to numerous matrix e...
Caporaso and Harris derive recursive formulas counting nodal plane
curves of degree d and geometric genus g in the plane (through the appropriate number of xed
general points). We rephrase their ar...
Counting real cubics with passage/tangency conditions
Counting real cubics passage/tangency conditions
2010/11/12
We study the following question: given a set of seven points and an immersed curve in the real plane R^2, all in general position, how many real rational nodal plane cubics pass through these points a...