Related papers: On the derived functors of the third symmetric-pow…

Some minor changes to the exposition.

In this paper, we obtain sharp bounds for the third Hankel determinants of the coefficients of the inverse of bounded turning functions. Thus answering a negatively to a conjecture recently posed regarding these functions. Additionally, we…

We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…

In this paper, we will define the derived 2-functor by projective resolution of any symmetric 2-group, and give some related properties of the derived 2-functor.

Through a brute-force approach to calculating the higher derivatives of the falling factorial function, a number of interesting quantities were obtained and analyzed. In particular, it was found that a quantity that can be described as the…

The original derivation of Power Functional Theory, Schmidt and Brader, JCP 138, 214101 (2013), is reworked in some detail with a view to clarifying and simplifying the logic and making explicit the various functional dependencies. We note…

We prove an asymptotic formula with power saving error term for a certain triple divisor sum.

We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…

We present a general method to obtain asymptotic power series for three kinds of sequences. And we give recurrence relations for determining the coefficients of asymptotic power series for these sequences. As applications, we show how these…

For a prime p>3, we compute a finite generating set for the SL_2(F_p)-invariants of the third symmetric power representation. The proof relies on the construction of an infinite SAGBI basis and uses the Hilbert series calculation of Hughes…

We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of extensions in the category of strict polynomial…

In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…

The rotational invariants constructed by the products of three spherical harmonic polynomials are expressed generally as homogeneous polynomials with respect to the three coordinate vectors, where the coefficients are calculated explicitly…

A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…

We develop a functorial approach to the study of the homotopy groups of spheres and Moore spaces $M(A,n)$, based on the Curtis spectral sequence and the decomposition of Lie functors as iterates of simpler functors such as the symmetric or…

We prove an asymptotic formula for the shifted convolution of the divisor functions $d_3(n)$ and $d(n)$, which is uniform in the shift parameter and which has a power-saving error term. The method is also applied to give analogous estimates…

Sums over inverse s-th powers of semiprimes and k-almost primes are transformed into sums over products of powers of ordinary prime zeta functions. Multinomial coefficients known from the cycle decomposition of permutation groups play the…

We prove a result, similar to the ones known as Ishihara's First and Second Trick, for sequences of functions.

Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented…

It is known that the Ehrhart polynomials of cross-polytopes, as well as of pyramids over them, have positive coefficients. We give a combinatorial proof of this fact by showing that a scaled version of the Ehrhart polynomials are generating…