The Ehrhart polynomial of the d-th hypersimplex Δ(d,n) of order n
is studied. By computational experiments and a known result for d=2, we
conjecture that the real part of every roots of the Ehrhart polynomial of
Δ(d,n) is negative and larger than −dn if n≥2d. In
this paper, we show that the conjecture is true when d=3 and that every root
a of the Ehrhart polynomial of Δ(d,n) satisfies −dn<Re(a)<1 if 4≤d≪n.Comment: 18 pages, 8 figure