… In this paper, we relate combinatorial conditions for polarizations of powers of the graded …
polarizations of powers of the graded maximal ideal into a condition about which sets of hook …

… We construct explicit such modules associated to any hook shape partitions. For the two …
to the effect of the operator Nabla on the corresponding hook-indexed Schur function, up to a …

… In general, the Computer Science literature assumes (either implicitily or explicitily) that a
social network is polarized if nodes can be partitioned into two highly cohesive subgroups, …

… Weyl [We] proved that the subring of “diagonal invariants” is generated by the polarized …
of (a, b)-cores (ie integer partitions in which no cell has hook length equal to a or b). Hence the …

… polarizations are shellable. We then give a novel characterization of polarizations of the same
class of ideals in terms of hook … rise to a polarization of a power of a graded maximal ideal. …

… partitions of $\{1,\dots ,n\}$ using a novel family of skein relations that resolve crossings in set
partitions. … To do this, we show that set partition skein relations arise naturally in the context …

… , for it provides a uniform partition of sentences into those that a generic subject S has to
believe in order to believe that ϕ ∅ ψ, and those that S has not. Still, the partition shares the …

… infrared fixed point, so that their partition functions with external sources become equal: …
screening of the defect charge by the vacuum polarization of the strongly coupled SQED theory. …

… The main difference between structural polarization scores is how they compute the
amount of polarization given a graph and its partition. As noted above, structural polarization …

… (\mathcal {Z}(G)\) and \(\mathcal {P}(G)\) are disjoint, but they do not necessarily form a
partitioning of V. We will often consider the partitioning of \(\mathcal {P}(G)\) by color, ie, the two …