- Bona’s Conjecture on Product of Cycles
- Conjecture of Thomas Lam on Affine NilCoxeter Algebras
- Pieri rule for toric Schur functions and Affine Stanley symmetric functions
- Let and . Let be the number of sequences with ‘s and ‘s, where , such that each occurs between the i-th and the j-th in the sequence. (Thus the total number of terms in each sequence is .) Then,
Problem 27 of http://math.mit.edu/~rstan/bij.pdf.
- The n-cube (as a graph) is the graph with vertex set (i.e., all binary n-tuples), with an edge between u and v if they differ in exactly one coordinate. Thus has vertices and edges. Then,
where c(G) is the number of spanning trees of G.
- Find a bijection between a staircase tableaux with no of size and perfect matchings of .
Conjectures on Cambrian Lattices and Generalized Associahedra – already resolved.
Cambrian Lattices – Nathan Reading
- Problem of finding volumes (Ehrhart polynomials) of valuation polytope (EC1 2nd ed. Exer. 4.62)
where and are long cycles, probability that 1 and 2 are in the same cycle of