human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "proof of a conjecture of klove on permutation codes under the chebychev distance"
  Abstract: Let d be a positive integer and x a real number. Let $$A_{d, x}$$Ad,x be a $$d\times 2d$$d×2d matrix with its entries $$\begin{aligned} a_{i,j}=\left\{ \begin{array}{ll} x\ \ &{} \quad \text{ for } \ 1\leqslant j\leqslant d+1-i,\\ 1\ \ &{} \quad \text{ for } \ d+2-i\leqslant j\leqslant d+i,\\ 0\ \ &{} \quad \text{ for } \ d+1+i\leqslant j\leqslant 2d. \end{array} \right. \end{aligned}$$ai,j=xfor1źjźd+1-i,1ford+2-iźjźd+i,0ford+1+iźjź2d.Further, let $$R_d$$Rd be a set of sequences of integers as follows: $$\begin{aligned} R_d=\left\{ (\rho _1, \rho _2,\ldots , \rho _d)|1\leqslant \rho _i\leqslant d+i, 1\leqslant i \leqslant d,\ \text{ and }\ \rho _r\ne \rho _s\ \quad \text{ for }\ r\ne s\right\} . \end{aligned}$$Rd=(ź1,ź2,ź,źd)|1źźiźd+i,1źiźd,andźrźźsforrźs.and define $$\begin{aligned} \Omega _d(x)=\sum _{\rho \in R_d}a_{1,\rho _1}a_{2, \rho _2}\ldots a_{d,\rho _d}. \end{aligned}$$Ωd(x)=źźźRda1,ź1a2,ź2źad,źd.In order to give a better bound on the size of spheres of permutation codes under the Chebychev distance, KlOve introduced the above function and conjectured that $$\begin{aligned} \Omega _d(x)=\sum _{m=0}^d{d\atopwithdelims ()m}(m+1)^d(x-1)^{d-m}. \end{aligned}$$Ωd(x)=źm=0ddm(m+1)d(x-1)d-m.In this paper, we settle down this conjecture positively.

Connected through hyperedge HE-1 (induced by source paper "improved lower bounds on the size of balls over permutations with the infinity metric"):
  with members:
    - "limited magnitude error correcting gray codes for rank modulation"
    - "compression in the space of permutations"
    - "new bounds for permutation codes in ulam metric"
    - "the bethe permanent of a nonnegative matrix"
    - "systematic error correcting codes for rank modulation"
    - "systematic codes for rank modulation"
    - "error correction in flash memories via codes in the ulam metric"
    - "snake in the box codes for rank modulation"

Question: Please tell me which class the center node belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.IT(Information Theory)