Related papers: Interval Decomposition of Infinite Zigzag Persiste…

Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in a linearly ordered set. Join-irreducible partitions into intervals are characterized in the lattice of all interval decompositions of…

Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers. The distribution of the number of summands converges to a Gaussian, and the individual measures on gaps between…

We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…

For any prime p, we construct, and simultaneously count, all of the complex Specht modules in a given p-block of the symmetric group which remain irreducible when reduced modulo p. We call the Specht modules with this property p-irreducible…

We give a decomposition as a direct sum of indecomposable modules of several types of Specht modules in characteristic $2$. These include the Specht modules labelled by hooks, whose decomposability was considered by Murphy. Since the main…

We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…

Four $\ZZ_+$-bigraded complexes with the action of the exceptional infinite-dimensional Lie superalgebra E(3,6) are constructed. We show that all the images and cokernels and all but three kernels of the differentials are irreducible…

Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies of $k$ interms of previous ones. In the case of embedding dimension at most $2$, we provided complete descriptions of all indecomposable summands of all syzygies…

In this note, we establish conditions under which the union of an increasing sequence of completely decomposable modules over domains are again completely decomposable. In our investigation, the condition of purity of modules is crucial. In…

Let G be a finite group, and let Omega:={t\in G\mid t^2=1}. Then Omega is a G-set under conjugation. Let k be an algebraically closed field of characteristic 2. It is shown that each projective indecomposable summand of the G-permutation…

Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

We define the notion of infinite friezes of positive integers as a variation of Conway-Coxeter frieze patterns and study their properties. We introduce useful gluing and cutting operations on infinite friezes. It turns out that…

We give a proof of the exponential uniform decay of magneto-elasticity waves in a compact medium

A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert…

We establish a bijection between torsion pairs in the category of finite-dimensional modules over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the Ziegler spectrum of A and a set I of indecomposable…

In this paper, we characterize smooth projective surfaces on which every integral pseudoeffective divisor has an integral Zariski decomposition.

We study countable sums of two dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be…

In this paper we expand on previous results, studying the extent to which one can detect fusion in certain finite groups $\Gamma$, from information about the universal deformation rings of absolutely irreducible…

We provide a definition of ephemeral multi-persistent modules and prove that the quotient of persistent modules by the ephemeral ones is equivalent to the category of $\gamma$-sheaves. In the case of one-dimensional persistence, our…