Alexis García Hurtado

Forced counts: when a symmetry group determines the discordance of a constructed ordering

We count the discordant pairs of an ordering against the binary order of the vertices of the n-cube, in the standard sense of rank correlation, and ask when that count is determined by the subgroup of the hyperoctahedral group B_n that the construction of the ordering respects. T...

Statistical Structure of the Historical Orderings of the I Ching Hexagrams: Pair Rule, Family Gradient, and the Limits of Demonstrability

The King Wen sequence orders the 64 hexagrams of the I Ching in an arrangement that has resisted explanation for three millennia. We present a statistical comparison of the three historical orderings (King Wen, Mawangdui, Jing Fang) against the binary ordering and against one ano...

Uninformative rungs: an order-theoretic stopping criterion for nested reference sets

When an object cannot be resampled and no generating process is available, a null hypothesis has to be built by declaring what may be permuted and what must be held fixed. The declaration is not unique, so the natural response is to report a family of nulls rather than one. A fam...