Related papers: Nahm sums, stability and the colored Jones polynom…
We introduce the concepts of marked multi-colorings, marked chromatic polynomials, and marked (multivariate) independence series for hypergraphs. We show that the coefficients of the q-th power of the marked independence series of a…
In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.
Given a continuous $n$-homogeneous polynomial $P\colon E\longrightarrow F$ between Banach spaces and $1\leq q\leq p<\infty$, in this paper we investigate some properties concerning lineability and spaceability of the $(p;q)$-summing set of…
We prove three results on the existence and structure of Nash equilibria for quasisupermodular games. A theorem is purely order-theoretic, and the other two involve topological hypotheses. Our topological results genralize Zhou's theorem…
The tail of the colored Jones polynomial of an alternating link is a $q$-series invariant whose first $n$ terms coincide with the first $n$ terms of the $n$-th colored Jones polynomial. Recently, it has been shown that the tail of the…
New results are added to the paper [4] about q-closed and solvable sesquilinear forms. The structure of the Banach space $\mathcal{D}[||\cdot||_\Omega]$ defined on the domain $\mathcal{D}$ of a q-closed sesquilinear form $\Omega$ is unique…
The aim of this work is to establish the existence, uniqueness and q-Gevrey character of formal power series solutions of q-analogues of analytic doubly-singular equations. Using a new family of Nagumo norms adapted for q-differences we…
Several new transformations for q-binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving…
Nash Q-learning may be considered one of the first and most known algorithms in multi-agent reinforcement learning (MARL) for learning policies that constitute a Nash equilibrium of an underlying general-sum Markov game. Its original proof…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
Quantum K-theory of a smooth projective variety at genus zero is a collection of integers that can be assembled into a generating series $J(Q,q,t)$ that satisfies a system of linear differential equations with respect to $t$ and…
Let $$ S_{m,n}(q):=\sum_{k=1}^{n}\frac{1-q^{2k}}{1-q^2} (\frac{1-q^k}{1-q})^{m-1}q^{\frac{m+1}{2}(n-k)}. $$ Generalizing the formulas of Warnaar and Schlosser, we prove that there exist polynomials $P_{m,k}(q)\in\mathbb{Z}[q]$ such that $$…
In this paper, we derive eight basic identities of symmetry in three variables related to $q$-Euler polynomials and the $q$-analogue of alternating power sums. These and most of their corollaries are new, since there have been results only…
The recent discovery of robust quantum anomalous Hall (QAH) effect in rhombohedral multilayer graphene (RMG) aligned with hexagonal boron nitride (hBN) has established a highly versatile platform for correlated topological matter. This…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
We consider the $k$-nested sum of integer powers, $F(n,m,k)$, defined as repeated partial sums of the classical Faulhaber polynomials. We provide an explicit recurrence relation relating $F(n,m,k)$ to sums of lower power $m-1$ and higher…
There are several questions one may ask about polynomials $q_m(x)=q_m(x;t)=\sum_{n=0}^mt^mp_n(x)$ attached to a family of orthogonal polynomials $\{p_n(x)\}_{n\ge0}$. In this note we draw attention to the naturalness of this partial-sum…
The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken…
The present paper is devoted to power series of SP type, i.e. with coefficients that are syntactically sum-product combinations. Apart from their applications to analytic knot theory and the so-called "Volume Conjecture", SP-series are…
We study the stability of black holes that are solutions of the dilaton gravity derived from string-theoretical models in two and five dimensions against to scalar field perturbations, using the Quasinormal Modes (QNMs) approach. In order…