We introduce the notions of layered semigroups and partial semigroups, and prove some Ramsey type partition results about them. These results generalize previous results of Gowers, Furstenberg, and of Bergelson, Blass, and Hindman. We give some applications of these results (see, e.g., Theorem 1.1) and present examples suggesting that our results are rather optimal.
Rather than referring to “minorities,” “members of minority groups” or “underrepresented minorities,” we should refer to such individuals as “minoritized.” Using “minoritized” makes it clear that being minoritized is about power and equity not numbers, connects racial oppression to the oppression of women, and gives us an easy way to conceive of intersectionality as being a minoritized member of a minoritized group. The term “minoritized” reveals the fact that white males and other dominant groups minoritize members of subordinated groups rather than obscuring this agency, describes microaggressions better than the term ‘microaggressions,’ and helps explain the need for solidarity within minoritized groups. It gives us a powerful way to promote racial justice by appealing to the common experience of being excluded. While using “minoritized” risks creating a false equivalence that sees all instances of being minoritized as equal and discounting unique forms of oppression by subsuming them under a single term, using this term carefully can ensure that its advantages outweigh these risks.
1Rado showed that a rational matrix is partition regular over N if and only if it satisfies the columns 2 condition. We investigate linear algebraic properties of the columns condition, especially for oriented 3 (vertex-arc) incidence matrices of directed graphs and for sign pattern matrices. It is established that 4 the oriented incidence matrix of a directed graph Γ has the columns condition if and only if Γ is strongly 5 connected, and in this case an algorithm is presented to find a partition of the columns of the oriented 6 incidence matrix with the maximum number of cells. It is shown that a sign pattern matrix allows the 7 columns condition if and only if each row is either all zeros or the row has both a + and −. 8 AMS subject classifications: (2010) 15A03, 05C50, 15B35, 05D10.9
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