Related papers: A note on Shintani's invariants
In this note, we rederive quantum Pieri's formula and the rim hook algorithm in quantum Schubert calculus by studying multiplication in the equivariant cohomology ring of Grassmannians with respect to equivariant Schubert classes which are…
We present an alternative $\mathbb{Q}$-form for Racinet's cyclotomic double shuffle Lie algebra, inspired by the double shuffle relations among congruent multiple zeta values studied by Yuan and Zhao. Our main result establishes an…
Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing $U_q(sl(2,\Rcc))$ at roots of unity. Its representations and the matrix elements are obtained. The dual of it is constructed and the corepresentations…
For any $\varepsilon > 0$ we derive effective estimates for the size of a non-zero integral point $m \in \mathbb{Z}^d \setminus \{0\}$ solving the Diophantine inequality $\lvert Q[m] \rvert < \varepsilon$, where $Q[m] = q_1 m_1^2 + \ldots +…
We establish an intriguing correspondence between a special set of classical solutions of the modified sinh-Gordon equation (i.e., Hitchin's "self-duality" equations) on a punctured Riemann sphere and a set of stationary states in the…
Quasi-shuffle algebras have been a useful tool in studying multiple zeta values and related quantities, including multiple polylogarithms, finite multiple harmonic sums, and q-multiple zeta values. Here we show that two ideas previously…
This article presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials for shapes that are naturally embedded in a torus. Then we…
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…
We study Hilbert's fourteenth problem from a geometric point of view. Nagata's celebrated counterexample demonstrates that for an arbitrary group action on a variety the ring of invariant functions need not be isomorphic to the ring of…
In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…
Connected the generalized Goncharov polynomials associated to a pair ($\partial,\mathcal{Z}$) if a delta operator $\partial$ and an interpolation grid $\mathcal{Z}$, introduced by Lorentz, Tringali and Yan in [7], with the theory of…
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this…
Formally self-adjoint, conformally covariant, polydifferential operators provide a general framework for studying variational problems, such as prescribing the scalar, $Q$-, or $\sigma_2$-curvatures, within a conformal class. We describe…
In this note we settle two open problems in the theory of permanents by using recent results from other areas of mathematics. Bapat conjectured that certain quotients of permanents, which generalize symmetric function means, are concave. We…
We show that the Einstein-Hilbert functional, as a functional on the space of Reeb vector fields, detects the vanishing Sasaki-Futaki invariant. In particular, this provides an obstruction to the existence of a constant scalar curvature…
A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…
H. J. S. Smith proved Fermat's two-square theorem using the notion of palindromic continuants. In this paper we extend Smith's approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on…
This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for…