combinatorics / Algebraic combinatorics
Reiner conjectured a description of the homotopy types of intervals in higher Bruhat orders. In corank $3$ it holds: the facial intervals of $B(n,n-3)$ are exactly the spherical intervals, and every other interval is contractible.
Temporal state
No reconciled state yet.
Append-only history
corank 3; the general conjecture remains open, corank 2 being McConville's case
Research memory
Reiner conjectured a description of the homotopy types of intervals in higher Bruhat orders. In corank $3$ it holds: the facial intervals of $B(n,n-3)$ are exactly the spherical intervals, and every other interval is contractible.
corank 3; the general conjecture remains open, corank 2 being McConville's case
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