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On the number of non-zero elements of joint degree vectors
(Electronic Journal of CombinatoricsThe Electronic Journal of Combinatorics, 2017-03-31)
Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 ≤ i ≤ j ≤ n-1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzero elements in a joint degree ...
Total Positivity in Markov Structures
(Institute of Mathematical StatisticsAnnals of Statistics, 2017-06)
We discuss properties of distributions that are multivariate totally positive of order two (MTP$_{2}$) related to conditional independence. In particular, we show that any independence model generated by an MTP$_{2}$ ...