Related papers: The Stanley-Stembridge Conjecture for $\bf 2 + 1 +…

With every reduced $E$-Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with zero morphisms $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$-algebras $\Bbbk…

The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in k[x_1,...,x_n] containing a homogeneous regular sequence f_1,...,f_n with deg(f_i)=a_i has the same Hilbert function as an ideal containing x_i^{a_i} for 1 \leq i \leq…

Deciding if a graph is a Hamilton graph, also named the Hamilton cycle problem, is important for discrete mathematics and computer science. Due to no characterization to identify Hamilton graphs effectively, there are no tractable…

In this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing that the primes contain arbitrarily long arithmetic progressions.…

Employing a quantum Monte Carlo simulation we find a pairing instability in the normal state of the infinite dimensional periodic Anderson model. Superconductivity arises from a normal state in which the screening is protracted and which is…

We show that one can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi…

Efficient simulation of the semiclassical Schr\"odinger equation has garnered significant attention in the numerical analysis community. While controlling the error in the unitary evolution or the wavefunction typically requires the time…

In this paper, we study the double shortcuts associated with pairs of standard hypercube decompositions of arbitrary Bruhat intervals in the symmetric group. Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025),…

The Delta Conjecture of Haglund, Remmel, and Wilson is a recent generalization of the Shuffle Conjecture in the field of diagonal harmonics. In this paper we give evidence for the Delta Conjecture by proving a pair of conjectures of Wilson…

In this article first we prove that a special case of the order ideal conjecture, originating from the work of Evans and Griffith in equicharacteristic, implies the monomial conjecture due to M. Hochster. We derive a necessary and…

The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…

We study a system of two hardcore bosonic Hubbard models weakly coupled with each other by tunneling. Assuming that the single uncoupled model exhibits off-diagonal long-range order, we prove that the coupled system exhibits spontaneous…

The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and…

This paper deals with the so-called Stanley conjecture, which asks whether they are non-isomorphic trees with the same symmetric function generalization of the chromatic polynomial. By establishing a correspondence between caterpillars…

We initiate an in-depth study of pattern avoidance on modified ascent sequences. Our main technique consists in using Stanley's standardization to obtain a transport theorem between primitive modified ascent sequences and permutations…

The extension of coupling constants to space-time dependent fields, the local couplings, makes possible to derive the non-renormalization theorems of supersymmetry by an algebraic characterization of Lagrangian N=1 supermultiplets. For…

Given an $\alpha > 1$ and a $\theta$ with unbounded continued fraction entries, we characterise new relations between Sturmian subshifts with slope $\theta$ with respect to (i) an $\alpha$-H\"oder regularity condition of a spectral metric,…

For $\frac{1}{2}<x<1$, $y>0$, and $n\in\mathbb{N}$, let $\displaystyle\theta_n(x+iy)=\sum_{i=1}^n\frac{{\mbox{sgn}}\, q_i}{q_i^{x+iy}}$, where $Q=\{q_1,q_2,q_3,\cdots\}$ is the set of finite products of distinct odd primes, and…

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…

We study the ribbon discs that arise from a symmetric union presentation of a ribbon knot. A natural notion of symmetric ribbon number is introduced and compared with the classical ribbon number. We show that the gap between these numbers…