Tootfinder

Type B Set partitions, an analogue of restricted growth functions
Amrita Acharyya
https://arxiv.org/abs/2404.14439 https://arxiv.org/…

Type B Set partitions, an analogue of restricted growth functions
In this work, we study type B set partitions for a given specific positive integer $k$ defined over $\langle n\rangle=\{-n, -(n-1),\cdots -1,0,1,\cdots n-1,n\}$. We found a few generating functions of type B analogue for some of the set partition statistics defined by Wachs, White and Steingrimsson for partitions over positive integers $[n] =\{1,2,\cdots n\}$, both for standard and ordered set partitions respectively. We extended the idea of restricted growth functions utilized by Wachs and Whi…

Universal graph series, chromatic functions, and their index theory
Tsuyoshi Miezaki, Akihiro Munemasa, Yusaku Nishimura, Tadashi Sakuma, Shuhei Tsujie
https://arxiv.org/abs/2403.09985

Universal graph series, chromatic functions, and their index theory
In the present paper, we introduce the concept of universal graph series. We then present four invariants of graphs and discuss some of their properties. In particular, one of these invariants is a generalization of the chromatic symmetric function and a complete invariant for graphs.

Quantum spin state stabilized by coupling with classical spins
Hironori Yamaguchi, Tsuyoshi Okubo, Akira Matsuo, Takashi Kawakami, Yoshiki Iwasaki, Taiki Takahashi, Yuko Hosokoshi, Koichi Kindo
https://arxiv.org/abs/2404.06767

Quantum spin state stabilized by coupling with classical spins
We introduce a model compound featuring a spin-1/2 frustrated square lattice partially coupled by spin-5/2. A significant magnetization plateau exceeding 60 T could be observed, indicating a quantum state formed by $S$ = 1/2 spins in the square lattice. The remaining $S$ = 5/2 spins exhibited paramagnetic behavior in the low-field regions. The numerical analysis confirmed that the observed quantum state is a many-body entangled state based on the dominant AF interactions and is strongly stabili…