Supersession history · C-0112
Every admissible two-row half-shifted cup coordinate is coefficientwise nonnegative
This lineage preserves 3 earlier results that led to the current listed result.
Read current walkthroughAll two-row-hook half-shifted cup coordinates are coefficientwise nonnegative
For every d>=n>=2, the gauged noncrossing-cup coordinate indexed by the two-row hook (n,1) for the flagged array A_(k,j)(a)=(k+1)h_(2j-k-1)(a,a+1,...,a+k+1) is a polynomial with nonnegative rational coefficients in b=a-1/2. It is positive for a>=1/2.
All (n,2) half-shifted cup coordinates are coefficientwise nonnegative
For every n>=2 and d>=max(n,3), the gauged noncrossing-cup coordinate indexed by the two-row partition (n,2) for the flagged array A_(k,j)(a)=(k+1)h_(2j-k-1)(a,a+1,...,a+k+1) is a polynomial with nonnegative rational coefficients in b=a-1/2. It is positive for a>=1/2.
All (n,3) half-shifted cup coordinates are coefficientwise nonnegative
For every n>=3 and d>=max(n,4), the gauged noncrossing-cup coordinate indexed by the two-row partition (n,3) for the flagged array A_(k,j)(a)=(k+1)h_(2j-k-1)(a,a+1,...,a+k+1) is a polynomial with nonnegative rational coefficients in b=a-1/2. It is positive for a>=1/2.
Every admissible two-row half-shifted cup coordinate is coefficientwise nonnegative
For every 1<=k<=n and d>=max(n,k+1), the gauged noncrossing-cup coordinate indexed by the two-row partition (n,k) for the flagged array A_(r,j)(a)=(r+1)h_(2j-r-1)(a,a+1,...,a+r+1) is a polynomial with nonnegative rational coefficients in b=a-1/2. It is strictly positive for a>=1/2.