Systems of distinct representatives and linear algebra

Abstract

So me purposes of thi s paper are: (1) To take se riously the term , " term rank. " (2) To ma ke an issue of not " rea rra nging rows a nd colu mns" by not "a rranging" the m in the firs t place. (3) To promote the nu merica l use of Cra mer 's rul e. (4) To ill us tra te that the re levance of " numbe r of s teps" to "a mount of wo rk" depends on the amount of work in a step. (5) To ca ll a tt ention to the com puta tional as pec t of SDR's, an aspect where the subjec t di ffe rs fro m bein g an instance of fa milia r li near algebra. (6) To describe a n SDR in s ta nce of a theory on extre mal co mbi nato rics tha t uses linea r algebra in ve ry dif· fe rent ways than does to tall y unimodular theory. (The preceding paper, Optimum Branc hings, de· sc ribes another instanc e of tha t theory.)