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We present a number of results about (finite) multiple harmonic sums modulo aprime, which provide interesting parallels to known results about multiple zetavalues (i.e., infinite multiple harmonic series). In particular, we prove a"duality" result for mod p multiple harmonic sums similar to (but distinctfrom) that for multiple zeta values. We also exploit the Hopf algebra structureof the quasi-symmetric functions to do calculations with multiple harmonic sumsmod p, and obtain, for each weight through 9, a set of generators for the spaceof weight-n multiple harmonic sums mod p. When combined with recent work, theresults of this paper offer significant evidence that the number of quantitiesneeded to generate the weight-n multiple harmonic series mod p is the n-thPadovan number (OEIS sequence A000931).Comment: 25 pages; version to appear in Kyushu J. Mat

QUASI-SYMMETRIC FUNCTIONS AND MOD <b><i>p </i></b>MULTIPLE HARMONIC SUMS