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Let $ X $ be an $ m \times n $ matrix of distinct indeterminates over a field$ K $, where $ m \le n $. Set the polynomial ring $K[X] := K[X_{ij} : 1 \le i\le m, 1 \le j \le n] $. Let $ 1 \le k < l \le n $ be such that $ l - k + 1 \gem $. Consider the submatrix $ Y_{kl} $ of consecutive columns of $ X $ from $ k$th column to $ l $th column. Let $ J_{kl} $ be the ideal generated by`diagonal monomials' of all $ m \times m $ submatrices of $ Y_{kl} $, wherediagonal monomial of a square matrix means product of its main diagonalentries. We show that $ J_{k_1 l_1} J_{k_2 l_2} \cdots J_{k_s l_s} $ has alinear free resolution, where $ k_1 \le k_2 \le \cdots \le k_s $ and $ l_1 \lel_2 \le \cdots \le l_s $. This result is a variation of a theorem due to Brunsand Conca. Moreover, our proof is self-contained, elementary and combinatorial.

Powers and products of monomial ideals related to determinantal ideals of maximal minors