  We show that the wave function of a one dimensional spinor gas with contact
$s$-wave interaction, either bosonic or fermionic, can be mapped to the direct
product of the wave function of a spinless Fermi gas with short-range $p$-wave
interaction and that of a spin system governed by spin parity projection
operators. Applying this mapping to strongly interacting spinor gases, we
obtain a generalized spin chain model that captures both the static and
dynamics properties of the system. Using this spin chain model, we investigate
the breathing mode frequency and the quench dynamics of strongly interacting
harmonically trapped spinor gases.
