相关论文: A partition identity connected to the second rank …

Recently, Pankaj Jyoti Mahanta and Manjil P. Saikika proved some identities relating certain restricted partitions into distinct odd parts with the partition whose odd parts are distinct combinatorially. They asked for the q-series proofs.…

The goal of this work is twofold: (i) to provide a detailed analysis of some categories of inductive graded ring - a concept introduced in [DM98] in order to provide a solution of Marshall's signature conjecture in the algebraic theory of…

We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by $m$, appearing fewer than $m$ times, or differing by less than $m$. We find results on their behavior and…

The aim of this note is to provoke discussion concerning arithmetic properties of function $p_{d}(n)$ counting partitions of an positive integer $n$ into $d$-th powers, where $d\geq 2$. Besides results concerning the asymptotic behavior of…

We prove new formulas and congruences for $p(n,k):=$ the number of partitions of $n$ into $k$ parts and $q(n,k):=$ the number of partitions of $n$ into $k$ distinct parts. Also, we give lower and upper bounds for the density of the set…

The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…

The restricted partitions in which the largest part is less than or equal to $N$ and the number of parts is less than or equal to $k$ were investigated by Andrews in \cite{Andrews76}. These partitions were extended recently by the author to…

The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…

This paper presents two case studies of data sets where the main inferential goal is to characterize time-varying patterns in model structure. Both of these examples are seen to be general cases of the so-called "partition problem," where…

By introducing $k$-marked Durfee symbols, Andrews found a combinatorial interpretation of $2k$-th symmetrized moment $\eta_{2k}(n)$ of ranks of partitions of $n$. Recently, Garvan introduced the $2k$-th symmetrized moment $\mu_{2k}(n)$ of…

This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.

A new kind of duality between the deep structures of spacetime and matter is proposed here, considering two partial orders which incorporate causality, extensity, and discreteness. This may have surprising consequences for the emergence of…

We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve…

In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost…

The number of sequences of odd length in strict partitions (denoted as $\mathrm{sol}$), which plays a pivotal role in the first paper of this series, is investigated in different contexts, both new and old. Namely, we first note a direct…

The goal of this note is to give a characterization of generalized quaternion $2$-groups by using their posets of cyclic subgroups.

In this note, we describe a family of particular algebraic, and nonquadratic, power series over an arbitrary finite field of characteristic 2, having a continued fraction expansion with all partial quotients of degree one. The main purpose…

The purpose of this note is to prove the $G$-equivariant Sarkisov program for a connected algebraic group $G$ following the proof of the Sarkisov program by Hacon and McKernan. As a consequence, we obtain a characterisation of connected…

We determine the partition dimension of the incidence graph $G(\Pi_q)$ of the projective plane $\Pi_q$ up to a constant factor $2$ as $(2+o(1))\log_2{q}\leq \mathrm{pd}(G(\Pi_q))\leq (4+o(1))\log_2{q}.$

A q-series with nonnegative power series coefficients is called positive. The partition statistics BG-rank is defined as an alternating sum of parities of parts of a partition. It is known that the generating function for the number of…