Zobrazeno 1 - 10
of 2 387
pro vyhledávání: '"Singh, Ajit"'
We confirm the speculation that the distribution of $t$-hooks among unrestricted integer partitions essentially descends to self-conjugate partitions. Namely, we prove that the number of hooks of length $t$ among the size $n$ self-conjugate partition
Externí odkaz:
http://arxiv.org/abs/2406.09059
Autor:
Amdeberhan, Tewodros, Singh, Ajit
A cubic partition consists of partition pairs $(\lambda,\mu)$ such that $\vert\lambda\vert+\vert\mu\vert=n$ where $\mu$ involves only even integers but no restriction is placed on $\lambda$. This paper initiates the notion of generalized cubic partit
Externí odkaz:
http://arxiv.org/abs/2404.06473
Autor:
Sengupta, Ritabrata, Singh, Ajit Iqbal
Finite dimensional entanglement for pure states has been used extensively in quantum information theory. Depending on the tensor product structure, even set of separable states can show non-intuitive characters. Two situations are well studied in the
Externí odkaz:
http://arxiv.org/abs/2402.14697
Autor:
Ono, Ken, Singh, Ajit
In his important 1920 paper on partitions, MacMahon defined the partition generating functions \begin{align*} A_k(q)=\sum_{n=1}^{\infty}\mathfrak{m}(k;n)q^n&:=\sum_{0< s_1
Externí odkaz:
http://arxiv.org/abs/2402.08783
In 2010, G.-N. Han obtained the generating function for the number of size $t$ hooks among integer partitions. Here we obtain these generating functions for self-conjugate partitions, which are particularly elegant for even $t$. If $n_t(\lambda)$ is
Externí odkaz:
http://arxiv.org/abs/2312.02933
Here we investigate the $q$-series \begin{align*} \mathcal{U}_a(q)&=\sum_{n=0}^{\infty} MO(a;n)q^n&:=\sum_{0< k_1
Externí odkaz:
http://arxiv.org/abs/2311.07496
Andrews and Newman introduced the mex-function $\text{mex}_{A,a}(\lambda)$ for an integer partition $\lambda$ of a positive integer $n$ as the smallest positive integer congruent to $a$ modulo $A$ that is not a part of $\lambda$. They then defined $p
Externí odkaz:
http://arxiv.org/abs/2303.03647
A resonating valence bond (RVB) state of a lattice of quantum systems is a potential resource for quantum computing and communicating devices. It is a superposition of singlet, i.e., dimer, coverings - often restricted to nearest-neighbour ones - of
Externí odkaz:
http://arxiv.org/abs/2302.09383
For a positive integer $t\geq 2$, let $b_{t}(n)$ denote the number of $t$-regular partitions of a nonnegative integer $n$. In a recent paper, Keith and Zanello investigated the parity of $b_{t}(n)$ when $t\leq 28$. They discovered new infinite famili
Externí odkaz:
http://arxiv.org/abs/2301.11192