Related papers: Wilson Theorems for Double-, Hyper-, Sub- and Supe…

We prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial's coefficients. This result extends to more general functions which we call "complex-exponent polynomials". To…

We prove a function field analogue of a conjecture of Schinzel on the factorization of univariate polynomials over the rationals. We derive from it a finiteness theorem for the irreducible factorizations of the bivariate Laurent polynomials…

We outline two methods of constructing improved composite operators using Wilson fermions.

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…

We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a…

We find a new duality for form factors of lightlike Wilson loops in planar $\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external…

Eigenvalues of a Wilson loop operator are gauge invariant and their distribution undergoes a transition at infinite N as the size of the loop is changed. We study this transition using the average characteristic polynomial associated with…

We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements…

We shall prove an extension of the semipositivity theorem for the case of reducible algebraic fiber spaces.

The article presents a generalization of Sherman-Morrison-Woodbury (SMW) formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).

We extend A.B. Mingarelli's method for constructing generalized factorials. Our extension uses a pair of arithmetic functions $(x, y)$, where $x$ is superadditive. When $x$ is the identity function, our generalized factorial reduces to…

Certain new inequalities for the sums of factorials are presented.

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and…

In this paper we describe the solutions of the functional equations expressing the addition theorems for sine and cosine on commutative hypergroups.

We give necessary and sufficient condition so that we have d-hypercyclicity for operators who map a holomorphic function to a partial sum of the Taylor expansion. This problem is connected with doubly universal Taylors series and this is an…

We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…

We generalize Philip Hall's celebrated theorems on finite solvable groups to scheme theory. Our result is based on a series of results on hypergroups.

We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

This paper contains the proof of Macdonald's duality and evaluation conjectures, the definition of the difference Fourier transform, the recurrence theorem generalizing Pieri rules, and the action of GL(2,Z) on the Macdonald polynomials at…