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A presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, Part II: quantum double Grothendieck polynomials

Forum of Mathematics, Sigma
In our previous paper, we gave a presentation of the torus-equivariant quantum K-theory ring $QK_{H}(Fl_{n+1})$ of the (full) flag manifold $Fl_{n+1}$ of type $A_{n}$ as a quotient of a polynomial ring by an explicit ideal.
Toshiaki Maeno, Satoshi Naito, Daisuke Sagaki +2 more
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Vanishing of Schubert coefficients via the effective Hilbert nullstellensatz

Forum of Mathematics, Sigma
Schubert Vanishing is a problem of deciding whether Schubert coefficients are zero. Until this work it was open whether this problem is in the polynomial hierarchy ${{\mathsf {PH}}}$ .
Igor Pak, Colleen Robichaux
doaj +1 more source

The quasisymmetric flag variety: A toric complex on noncrossing partitions

Forum of Mathematics, Pi
We develop the geometric theory of equivariant quasisymmetry via a new “quasisymmetric flag variety.” This is a toric complex in the flag variety whose fixed point set is the set of (algebraic) noncrossing partitions, and whose cohomology ring is the ...
Nantel Bergeron +4 more
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Smooth surfaces with maximally many lines

Forum of Mathematics, Sigma
We prove that a smooth projective surface of degree d in P3 $\mathbb P^3$ double struck upper P cubed contains at most d2(d2−3d+3) $d^2(d^2-3d+3)$ d squared left parenthesis d squared minus 3 d plus 3 right parenthesis lines.
Janet Page, Tim Ryan, Karen E. Smith
doaj +1 more source

Unravelling adolescent girls' aspirations in Nepal: Status and associations with individual-, household-, and community-level characteristics. [PDF]