Related papers: Simple proofs and expressions for the restricted p…
This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
Define a "nuclear partition" to be an integer partition with no part equal to one. In this study we prove a simple formula to compute the partition function $p(n)$ by counting only the nuclear partitions of $n$, a vanishingly small subset…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
We prove partial regularity for minimizers of vectorial integrals of the Calculus of Variations, with general growth condition, imposing quasiconvexity assumptions only in an asymptotic sense.
We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic…
Stanley's theory of $(P,\omega)$-partitions is a standard tool in combinatorics. It can be extended to allow for the presence of a restriction, that is a given maximal value for partitions at each vertex of the poset, as was shown by Assaf…
We derive the mean square of the divisor function using only elementary techniques.
Integer partitions express the different ways that a positive integer may be written as a sum of positive integers. Here we explore the analytic properties of a new polynomial $f_\lambda(x)$ that we call the partition polynomial for the…
Extending Sellers' result, Das et al. recently proved some congruence results for generalized overcubic partitions using theta functions and posed some related conjectures. In this paper, we provide a combinatorial proof of a result in…
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
The functional calculus for normal elements in $C^*$-algebras is an important tool of analysis. We consider polynomials $p(a,a^*)$ for elements $a$ with small self-commutator norm $\|[a,a^*]\| \le \delta$ and show that many properties of…
We introduce the ramified partition algebra, which is a physically motivated and natural generalization of the partition algebra. We investigate its representation theory and demonstrate quasi--heredity under certain conditions. Under these…
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
It is shown that a piecewise linear function can be represented as a Max-Min polynomial of its linear components.
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
We find general solutions to the generating-function equation sum c_q^{(X)} z^q = F(z)^X, where X is a complex number and F(z) is a convergent power series with |F(0)| >0. We then use these results to derive finite expressions containing…
Elementary proofs are given for sums of Schur functions over partitions into at most n parts each less than or equal to m for which i) all parts are even, ii) all parts of the conjugate partition are even. Also, an elementary proof of a…