Infinite symmetric group and combinatorial descriptions of semigroups of   double cosets
  We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs, two-dimensional surfaces with polygonal tiling) and describe explicitly the multiplications. 
Yury A. Neretin
math.RT math.CO math.GR