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We give a direct combinatorial proof of the $q,t$-symmetry relation $\tildeH_{\mu}(X;q,t)=\tilde H_{\mu'}(X;t,q)$ in the Macdonald polynomials $\tildeH_\mu$ at the specialization $q=1$. The bijection demonstrates that theMacdonald inv statistic on the permutations of any given row of a Young diagramfilling is Mahonian. Moreover, our bijection gives rise a family of newbijections on words that preserves the classical Mahonian inv statistic.

Macdonald symmetry at $q=1$ and a new class of inv-preserving bijections on words