Related papers: Kostka semigroups and generalized Dyck paths

We consider decompositions of digraphs into edge-disjoint paths and describe their connection with the $n$-th Weyl algebra of differential operators. This approach gives a graph-theoretic combinatorial view of the normal ordering problem…

In this paper we reduce the generalized Hilbert's third problem about Dehn invariants and scissors congruence classes to the injectivity of certain Chern--Simons invariants. We also establish a version of a conjecture of Goncharov relating…

Let $G$ be a locally finite group and $F(G)$ the Hirsch--Plotkin radical of $G$. Denote by $S$ the full inverse image of the generalized Fitting subgroup of $G/F(G)$ in $G$. Assume that there is a number $k$ such that the length of every…

An odd-dimensional version of the Goldberg conjecture was formulated and proved by Boyer and Galicki, using an orbifold analogue of Sekigawa's formulas, and an approximation argument of K-contact structures with quasi-regular ones. We…

The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables is introduced that…

We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety $X$ over a field $k$, a $k$-smooth divisor $D \subset X$, and a reductive $X$-group $G$ whose base change $G_D$ is totally isotropic,…

In this paper we consider the problem of Galois descent for suitably completed algebraic K-theory of fields. One of the main results is a suitable form of rigidity for Borel-style generalized equivariant cohomology with respect to certain…

We introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group $S_n$ on the cohomology of Hessenberg varieties extends to generalized Hessenberg varieties and that natural…

We discuss some variants of cone theorem for movable curves in any codimensions.

Bott periodicity for the unitary, orthogonal and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients similar periodicity results are…

We prove the Schr\"oder case, i.e. the case $\langle \cdot,e_{n-d}h_d \rangle$, of the conjecture of Haglund, Remmel and Wilson (Haglund et al. 2018) for $\Delta_{h_m}\Delta_{e_{n-k-1}}'e_n$ in terms of decorated partially labelled Dyck…

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…

In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) are reproduced and broadly generalized. Among many new results the…

Generalizing the notion of Newton polytope, we define the Newton-Okounkov body, respectively, for semigroups of integral points, graded algebras, and linear series on varieties. We prove that any semigroup in the lattice Z^n is…

Decomposition complexity for metric spaces was recently introduced by Guentner, Tessera, and Yu as a natural generalization of asymptotic dimension. We prove a vanishing result for the continuously controlled algebraic K-theory of bounded…

Motivated by the Farrell-Jones Conjecture for group rings, we formulate the $\mathcal{C}$op-Farrell-Jones Conjecture for the K-theory of Hecke algebras of td-groups. We prove this conjecture for (closed subgroups of) reductive p-adic groups…

In projective algebraic geometry, there are classical and fundamental results that describe the structure of geometry and syzygies, and many of them characterize varieties of minimal degree and del Pezzo varieties. In this paper, we…

In this study, we refine the compactification presented by Witz \cite{Witz} for general semigroups to the case of bounded $C_0$-semigroups, involving adjoint theory for this class of operators. This approach considerably reduces the…

Klimo\v{s}ov\'a, Piguet, and Rozho\v{n} conjectured that any graph with minimum degree $k/2$ and sufficiently many vertices of degree $k$ should contain all trees with $k$ edges. We prove an asymptotic version of this conjecture for dense…

We prove the cohomological purity of punctual Hilbert schemes of points on generic irreducible planar curve singularities, by constructing an explicit affine paving. Via their identification with generalized $GL_N$-affine Springer fibers…