
QUASISYMMETRIC FUNCTIONS AND MOD p MULTIPLE HARMONIC SUMSQUASISYMMETRIC FUNCTIONS AND MOD p MULTIPLE HARMONIC SUMSAA10994346 
"/Hoffman, Michael E./"Hoffman, Michael E.
69
(
2
)
, pp.345

366 , 20151013 , Faculty of Mathematics, Kyushu University
ISSN:13406116
NCID:AA10994346
Description
We present a number of results about (finite) multiple harmonic sums modulo a prime, which provide interesting parallels to known results about multiple zeta values (i.e. infinite multiple harmonic series). In particular, we prove a 'duality' result for mod p harmonic sums similar to (but distinct from) that for multiple zeta values. We also exploit the Hopf algebra structure of the quasisymmetric functions to perform calculations with multiple harmonic sums mod p, and obtain, for each weight n through nine, a set of generators for the space of weightn multiple harmonic sums mod p. When combined with recent work, the results of this paper offer significant evidence that the number of quantities needed to generate the weightn multiple harmonic sums mod p is the nth Padovan number (OEIS sequence A000931).