Related papers: Crystal rules for $(\ell,0)$-JM partitions

We prove new formulas for $p_d(n)$, the number of $d$-ary partitions of $n$, and, also, for its polynomial part. Given a partition $\lambda=(\lambda_1,\ldots,\lambda_{\ell})$, its associated $j$-th symmetric elementary partition,…

We present the first lattice QCD determination of the $\Lambda \to N$ vector and axial-vector form factors, which are essential inputs for studying the semileptonic decay $\Lambda \to p \ell \bar{\nu}_\ell$. This channel provides a clean,…

We prove that if $e$ is a join-irreducible element of a semimodular lattice $L$ of finite length and $h<e$ in $L$ such that $e$ does not cover $h$, then $e$ can be "lowered" to a covering of $h$ by taking a length-preserving semimodular…

In analogy with the semi-Fibonacci partitions studied recently by Andrews, we define semi-Pell compositions and semi-$m$-Pell compositions. We find that these are in bijection with certain weakly unimodal $m$-ary compositions. We give…

Motivated by the study of integer partitions, we consider partitions of integers into fractions of a particular form, namely with constant denominators and distinct odd or even numerators. When numerators are odd, the numbers of partitions…

The dimension of an irreducible representation of $GL(n,\mathbb{C})$, $Sp(2n)$, or $SO(n)$ is given by the respective hook-length and content formulas for the corresponding partition. The first author, inspired by the Nekrasov-Okounkov…

Certain mathematical structures make a habit of reoccuring in the most diverse list of settings. Some obvious examples exhibiting this intrusive type of behavior include the Fibonacci numbers, the Catalan numbers, the quaternions, and the…

PED partitions are partitions with even parts distinct while odd parts are unrestricted. Similarly, POD partitions have distinct odd parts while even parts are unrestricted. Merca proved several recurrence relations analytically for the…

We introduce a semisimple tensor category $\mc{O}^{int}_q(m|n)$ of modules over an quantum ortho-symplectic superalgebra. It is a natural counterpart of the category of finitely dominated integrable modules over the quantum classical…

The paper first covers several properties of the extension of the divisibility relation to a set ${}^*\hspace{-0.5mm}N$ of nonstandard integers. After that, a connection is established with the divisibility in the Stone-\v{C}ech…

We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we…

In a previous paper, the authors studied the radical filtration of a Weyl module $\Delta_\zeta(\lambda)$ for quantum enveloping algebras $U_\zeta(\overset\circ{\mathfrak g})$ associated to a finite dimensional complex semisimple Lie algebra…

We present a lattice-QCD determination of the $\Lambda \to p$ vector and axial-vector form factors, providing theoretical input for studies of the semileptonic decay $\Lambda \to p\ell\bar{\nu}_\ell$. The calculation is carried out on a…

In this paper we use some basic facts from the theory of (matrix) Lie groups and algebras to show that many of the classical matrix splittings used to construct stationary iterative methods and preconditioniers for Krylov subspace methods…

Taking into account the $\Lambda$ baryon distribution amplitudes and the most general form of the interpolating current of the $\Lambda_{b}$, the semileptonic $\Lambda_{b}\rar \Lambda \ell^+\ell^- $ transition is investigated in the…

For L a finite lattice, let C(L) denote the set of pairs g = (g_0,g_1) such that g_0 is a lower cover of g_1 and order it as follows: g <= d iff g_0 <= d_0, g_1 <= d_1, but not g_1 <= d_0. Let C(L,g) denote the connected component of g in…

In this paper, we present, given a odd integer $d$, a decomposition of the multiset of bar lengths of a bar partition $\lambda$ as the union of two multisets, one consisting of the bar lengths in its $\bar{d}$-core partition…

In 2017, Keith presented a comprehensive survey on integer partitions into parts that are simultaneously regular, distinct, and/or flat. Recently, the authors initiated a study of partitions into parts that are simultaneously regular and…

We investigate the set of partial partitions of a finite set, ordered by inclusion. With this ordering the set of partial partitions can be studied as an abstract simplicial complex. We use the theory of shellable nonpure complexes to find…

Let $k$ be an algebraically closed field. Let $\Lambda$ be a noetherian commutative ring annihilated by an integer invertible in $k$ and let $\ell$ be a prime number different from the characteristic of $k$. We prove that if $X$ is a…