The squarefree Veronese Stanley depth formula conjecture

Let KK be a field, let S=K[x1,,xn]S=K[x_1,\dots,x_n], and let In,dI_{n,d} be the ideal generated by all squarefree monomials of degree dd in SS. For positive integers dd and nn with 1dn1\leq d\leq n, write sdepth(In,d)\operatorname{sdepth}(I_{n,d}) for its Stanley depth. Squarefree Veronese Stanley depth conjecture. For every 1dn1\leq d\leq n,

sdepth(In,d)=(nd+1)(nd)+d.\operatorname{sdepth}(I_{n,d})=\left\lfloor\frac{\binom{n}{d+1}}{\binom{n}{d}}\right\rfloor+d.

This conjecture generalizes the paper's main theorem and is supported by the bounds and cases established there. The source does not give a resolution status for the full formula.

Sources & referencesView supporting material

Primary source

Mitchel T. Keller, Yi-Huang Shen, Noah Streib and Stephen J. Young, “On the Stanley Depth of Squarefree Veronese Ideals”, arXiv:0910.4645 (2009).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.