Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
5 problems
If r is odd, a basis of MR^sharp will be parametrized by colored compositions such that parts of color 0 are not ≡ 0 bmod r and parts of color 1 are arbitrary. The Hilbert series is then H_r(t)=frac1-t^r1-2(t+t^2+… +t^r). If r is even,…
For each n, there exists a term order such that a code is 0- or 1-inductively pierced if and only if the reduced Gröbner basis contains binomials of degree 2 or less.
If a neural code is labeled such that the i^th neuron is added as a piercing at the i^th step, then its toric ideal has a quadratic Gröbner basis with respect to the term order prec.
There is an isomorphism of graded S_n-modules R_n,k,r≅ R_n,k,r' .
Let \alpha, \beta and \mu be partitions of the same size. The generating function \sum_{N \ge 0} L_{N\alpha,N\beta}^{N\mu}(q) t^N is a rational function of q and t.