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Putnam 2018 A2

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December 2, 2018
PutnamPutnam 2018determinant

Problem Statement

Let S1,S2,…,S2n−1S_1, S_2, \dots, S_{2^n - 1} be the nonempty subsets of {1,2,…,n}\{1, 2, \dots, n\} in some order, and let MM be the (2n−1)×(2n−1)(2^n - 1) \times (2^n - 1) matrix whose (i,j)(i, j) entry is mij={0if Si∩Sj=∅,1otherwise.m_{ij} = \left\{ \begin{array}{cl} 0 & \text{if $S_i \cap S_j = \emptyset$}, \\ 1 & \text{otherwise}. \end{array} \right. Calculate the determinant of MM.
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