Related papers: Presentations for (singular) partition monoids: a …
We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and…
The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existence of $\mathcal{U}$-small partitions of unity (partitions…
The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands,…
In this article we give explicit descriptions of the multiplicities of some classes of monomial ideals. For instance, we give a formula for the multiplicities of all codimension 1 monomial ideals, and another formula for the multiplicities…
In this paper, we consider graded near-rings over a monoid $G$ as a generalizations of graded rings over groups. We introduce certain innovative graded prime ideals and study some of its basic properties over graded near-rings.
We construct finite coherent presentations of plactic monoids of type A. Such coherent presentations express a system of generators and relations for the monoid extended in a coherent way to give a family of generators of the relations…
Multiplier ideals, and the vanishing theorems they satisfy, have found many applications in recent years. In the global setting they have been used to study pluricanonical and other linear series on a projective variety. More recently, they…
Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal. The pruned resolution is not simplicial in…
This is a self-contained review of a new approach to soliton equations of KdV type developed by the author together with B. Feigin and B. Enriquez.
In this paper we present a new class of integer partition identities. The number of partitions with d-distant parts can be represented as a sum of the number of partitions with 1-distant parts whose even parts are greater than twice the…
We obtain a new presentation for Specht modules whose conjugate shapes have strictly decreasing parts by introducing a linear operator on the space generated by column tabloids. The generators of the presentation are column tabloids and the…
We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are…
The present notes are the expanded and polished version of three lectures given in Stanford, concerning the analytic and arithmetic properties of weight one modular forms. The author tried to write them in a style accessible to…
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…
We establish a new, fairly general cancellativity criterion for a presented monoid that properly extends the previously known related criteria. It is based on a new version of the word transformation called factor reversing, and its…
In his paper, "On a Partition Function of Richard Stanley," George Andrews proves a certain partition identity analytically and asks for a combinatorial proof. This paper provides the requested combinatorial proof.
We argue that the invariant tensor field introduced in [1] is unique under the condition that the invariant spin field is unique, and thereby complete that part of the discussion in that paper.
This is an expository paper on the characterization of the even (or odd) smooth homogeneous convolution Calder\'on-Zygmund operators in R^n such that the maximal singular integral can be controlled in the L^2 norm by the singular integral.…