human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "on the ingleton violations in finite groups"):
  Abstract: Given $n$ discrete random variables, its entropy vector is the $2^n-1$ dimensional vector obtained from the joint entropies of all non-empty subsets of the random variables. It is well known that there is a one-to-one correspondence between such an entropy vector and a certain group-characterizable vector obtained from a finite group and $n$ of its subgroups [3]. This correspondence may be useful for characterizing the space of entropic vectors and for designing network codes. If one restricts attention to abelian groups then not all entropy vectors can be obtained. This is an explanation for the fact shown by Dougherty et al [4] that linear network codes cannot achieve capacity in general network coding problems. All abelian group-characterizable vectors, and by fiat all entropy vectors generated by linear network codes, satisfy a linear inequality called the Ingleton inequality. It is therefore of interest to identify groups that violate the Ingleton inequality. In this paper, we study the problem of finding nonabelian finite groups that yield characterizable vectors which violate the Ingleton inequality. Using a refined computer search, we find the symmetric group $S_5$ to be the smallest group that violates the Ingleton inequality. Careful study of the structure of this group, and its subgroups, reveals that it belongs to the Ingleton-violating family $PGL(2,q)$ with a prime power $q \geq 5$, i.e., the projective group of $2\times 2$ nonsingular matrices with entries in $\mathbb{F}_q$. We further interpret this family using the theory of group actions. We also extend the construction to more general groups such as $PGL(n,q)$ and $GL(n,q)$. The families of groups identified here are therefore good candidates for constructing network codes more powerful than linear network codes, and we discuss some considerations for constructing such group network codes.

Includes members:
  Member "entropy region and convolution":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "how to use undiscovered information inequalities direct applications of the copy lemma")
  Member "finite p groups entropy vectors and the ingleton inequality for nilpotent groups":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "mapping the region of entropic vectors with support enumeration information geometry")
  Member "non shannon information inequalities in four random variables":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the storage cost of private information retrieval")
  Member "linear rank inequalities on five or more variables":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "characteristic dependent linear rank inequalities via complementary vector spaces")
  Member "group characterizable entropy functions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "bag query containment and information theory")

Question: Please tell me which class the source paper 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)