Related papers: Answering Two OPAC Problems Involving Banff Quiver…

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…

Let $n \geq 2$. We introduce the notion of $n$-representations of quivers, and we explicitly provide concrete examples of $2$-representations of quivers. We establish the categories of $n$-representations and investigate kernels and…

We investigate the problem of classifying the Banach spaces $\mathrm{Lip}_0(C(K))$ for Hausdorff compacta $K$. In particular, sufficient conditions are established for a space $\mathrm{Lip}_0(C(K))$ to be isomorphic to…

The existence of one-way functions (OWFs) forms the minimal assumption in classical cryptography. However, this is not necessarily the case in quantum cryptography. One-way puzzles (OWPuzzs), introduced by Khurana and Tomer, provide a…

It has been noticed since around 2007 that certain enumeration problems can be solved when an analytic or algebraic curve is identified. This curve is the key to the problem. In these lectures, a few such examples are presented. One is a…

We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with characteristic different from 2. It turns out that there are infinite families of isomorphism classes of pointed Hopf…

We deal with some pcf investigations mostly motivated by abelian group theory problems and deal their applications to test problems (we expect reasonably wide applications). We prove almost always the existence of aleph_omega-free abelian…

Valiant's 1984 paper is widely credited with introducing the PAC learning model, but it, in fact, introduced a different model: unlike PAC learning, the learner receives only positives, may issue membership queries, and must output a…

We study a family of equivalence relations on $S_n$, the group of permutations on $n$ letters, created in a manner similar to that of the Knuth relation and the forgotten relation. For our purposes, two permutations are in the same…

We study the $m$-graded quiver theories associated to CY $(m+2)$-folds and their order $(m+1)$ dualities. We investigate how monodromies give rise to mutation invariants, which in turn can be formulated as Diophantine equations…

Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…

Many conjectures and open problems in graph theory can either be reduced to cubic graphs or are directly stated for cubic graphs. Furthermore, it is known that for a lot of problems, a counterexample must be a snark, i.e. a bridgeless cubic…

Although symmetric informationally complete positive operator valued measures (SIC POVMs, or SICs for short) have been constructed in every dimension up to 67, a general existence proof remains elusive. The purpose of this paper is to show…

Starting from a collection of line bundles on a projective toric orbifold X, we introduce a stacky analogue of the classical linear series. Our first main result extends work of King by building moduli stacks of refined representations of…

Motivated from the complete solution of important $abc$-problem for Gabor system for the Hilbert space $\mathcal{L}^2(\mathbb{R})$ by Dai and Sun [\textit{Memoirs of Amer. Math. Soc., 2016}] and from the existential result of approximate…

A series invariant for a certain class of closed 3-manifolds associated with a type I Lie superalgebra sl(m|n) was introduced recently. We find a q-series for the other Lie superalgebra of the same type of the minimum rank.

We divide the class of infinite computable trees into three types. For the first and second types, $0'$ computes a nontrivial self-embedding while for the third type $0''$ computes a nontrivial self-embedding. These results are optimal and…

We discuss unoriented quivers with flavour that arise from D3-branes at local orbifold singularities, in the presence of Omega-planes and non-compact D7-branes. We produce a wide class of unoriented quiver gauge theories, including new…

Recently, Ballantine and Welch considered various generalizations and refinements of POD and PED partitions. These are integer partitions wherein the odd parts must be distinct (in the case of POD partitions) or the even parts must be…

We study elliptic curves of the form $x^3+y^3=2p$ and $x^3+y^3=2p^2$ where $p$ is any odd prime satisfying $p\equiv 2\bmod 9$ or $p\equiv 5\bmod 9$. We first show that the $3$-part of the Birch-Swinnerton-Dyer conjecture holds for these…