Related papers: Linear independence of powers

We give an elementary proof of the theorem which states that a finite unramified algebra over a discrete field is tracically \'etale. -- Nous donnons une d\'emonstration \'el\'ementaire du th\'eor\`eme selon lequel toute alg\`ebre nette sur…

In [CCHT25], the authors introduced multiple Eisenstein series of arbitrary rank in positive characteristic and the $q$-shuffle algebra $\mathcal{E}$ associated with them. In the present paper, we establish a class of linear independence…

We present further developments on the Lagrangian 1-form description for one-dimensional integrable systems in both discrete and continuous levels. A key feature of integrability in this context called a closure relation will be derived…

We prove that among 1 and the odd zeta values $\zeta(3)$, $\zeta(5)$, \ldots, $\zeta(s)$, at least $ 0.21 \sqrt{s}/\sqrt{\log s}$ are linearly independent over the rationals, for any sufficiently large odd integer $s$. This is the first…

We provide a closed formula for the graded Betti numbers in the linear strands of all powers of binomial edge ideals $J_G$ arising from closed graphs $G$ that do not have the complete graph $K_4$ as an induced subgraph. We show that these…

In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in $L^2(\mathbb R^d)$. Our proof is based on a simple argument from the…

Motivated by algorithmic problems from combinatorial group theory we study computational properties of integers equipped with binary operations +, -, z = x 2^y, z = x 2^{-y} (the former two are partial) and predicates < and =. Notice that…

The independence number of a hypergraph H is the size of a largest set of vertices containing no edge of H. In this paper, we prove new sharp bounds on the independence number of n-vertex (r+1)-uniform hypergraphs in which every r-element…

Using appropriate power series evaluations, we determine all moments of arbitrary positive powers of the arcsine. As consequences we evaluate several doubly infinite classes of power series involving central binomial coefficients and…

Let $q_1, \ldots , q_t$ be distinct prime numbers. Let $a_1, \ldots , a_t$ be nonnegative integers. We establish effective lower bounds for $|z^d - q_1^{a_1} \ldots q_t^{a_t}|$ and for its greatest prime factor, which tend to infinity with…

Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials {f_1, ..., f_m} \subset \F[x_1, ..., x_n] are called algebraically independent if there is…

Let A be a regular domain of dimension d containing an infinite field and let n be an integer with 2n\geq d+3. For a stably free A-module P of rank n, we prove that (i) P has a unimodular element if and only if the euler class of P is zero…

In 2009, Shur published the following conjecture: Let $L$ be a power-free language and let $e(L)\subseteq L$ be the set of words of $L$ that can be extended to a bi-infinite word respecting the given power-freeness. If $u, v \in e(L)$ then…

In this paper, the notion of conditionally bi-free independence for pairs of algebras is introduced. The notion of conditional $(\ell, r)$-cumulants are introduced and it is demonstrated that conditionally bi-free independence is equivalent…

We study the zero sets of the independence polynomial on recursive sequences of graphs. We prove that for a maximally independent starting graph and a stable and expanding recursion algorithm, the zeros of the independence polynomial are…

We present a description of electrons propagating in an elliptically polarised plane wave background which includes circular and linear polarisations as special cases. We calculate to all orders in the background field the two point…

Let G be a linear group such that for every g in G there is a finite set R(g) with the property that for every x in G all sufficiently long commutators [g,x,x,...,x] belong to R(g). It is proved that G is finite-by-hypercentral.

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…

We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the…

We obtain a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms. The key fact is that the multiplier (i.e. the factor $M$ in the differential equation $dS=MS$) has only…