Partial Rank Symmetry of Distributive Lattices for Fences

  title={Partial Rank Symmetry of Distributive Lattices for Fences},
  author={Sergi Elizalde and Bruce E. Sagan},
  journal={Annals of Combinatorics},
Associated with any composition β = (a, b, . . .) is a corresponding fence poset F (β) whose covering relations are x1 ✁ x2 ✁ . . .✁ xa+1 ✄ xa+2 ✄ . . .✄ xa+b+1 ✁ xa+b+2 ✁ . . . . The distributive lattice L(β) of all lower order ideals of F (β) is important in the theory of cluster algebras. In addition, its rank generating function r(q;β) is used to define q-analogues of rational numbers. Oğuz and Ravichandran recently showed that its coefficients satisfy an interlacing condition, proving a… 
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