Related papers: Integrity of ghosts
Implementation bugs threaten the soundness of algorithmic software verifiers. Generating correctness certificates for correct programs allows for efficient independent validation of verification results, and thus helps to reveal such bugs.…
We consider conjugation action of symmetric group on the semigroup of all partial functions and develop a machinery to investigate character formulas and multiplicities. In particular, we determine nilpotent matrices whose orbit under…
We introduce a new homological machine for the study of secondary geometric invariants. The objects, called spark complexes, occur in many areas of mathematics. The theory is applied here to establish the equivalence of a large family of…
We develop cycle index generating functions for orthogonal groups in even characteristic, and give some enumerative applications. A key step is the determination of the values of the complex linear-Weil characters of the finite symplectic…
We establish how the coefficients of a sparse polynomial system influence the sum (or the trace) of its zeros. As an application, we develop numerical tests for verifying whether a set of solutions to a sparse system is complete. These…
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite…
We associate with a matrix over an arbitrary field an infinite family of matrices whose sizes vary from one to infinity; their entries are traces of powers of the original matrix. We explicitly evaluate the determinants of matrices in our…
This manuscript contains tables giving the multiplicities with which irreducible characters of exceptional Weyl groups appear in characters induced from certain reflection subgroups containing maximal parabolic subgroups.
Numerical simulations of cluster mergers reveal many characteristics of the merging process: shock structure and strength, observational signatures of the dynamical state, effects on the mass determination, turbulence and the evolution of…
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
Traces of singular moduli can be approximated by exponential sums of quadratic irrationals. Recently Andersen and Duke used theory of Maass forms to estimate generalized twisted traces with power-saving error bounds. We establish an…
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
In view of applications to conformal field theory or to other branches of theoretical physics and mathematics, new examples of character tables for Drinfeld doubles of finite groups (modular data) are made available on a website.
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
We give a lower bound of the cochain type level of the diagonal map on the classifying space of a Lie group by using the ghostness of a shriek map. Moreover, in a derived category, we discuss the triviality of the shriek map which induces…
We recently introduced the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. There is a type of idempotent system, said to be symmetric. In the present paper we classify up…
Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks