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SUMMARY:Qi CHEN (Xidian University)
DTSTART:20250212T140000Z
DTEND:20250212T151500Z
DTSTAMP:20260423T053135Z
UID:AAIT/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AAIT/43/">Ma
 troidal entropy functions (Part 1)</a>\nby Qi CHEN (Xidian University) as 
 part of Seminar on Algorithmic Aspects of Information Theory\n\n\nAbstract
 \nA matroidal entropy function is an entropy function in the form log v ·
  r_M \, where v is an integer exceeding one and r_M is the rank function o
 f a matroid M. For a matroid M\, the characterization of matroidal entropy
  functions induced by M is to determine its probabilistic-characteristic s
 et Χ_M\, i.e.\, the set of integers v such that log v · r_M is entropic.
  When M is a connected matroid with rank not less than 2\, such characteri
 zation also determines the entropic region on the extreme ray of the polym
 atroidal region containing log v · r_M.\n\nTo characterize matroidal entr
 opy functions\, variable-strength orthogonal arrays (VOA) is defined\, whi
 ch can be considered as special cases of classic combinatorial structure o
 rthogonal arrays (OA). It can be proved that whether log v · r_M is entro
 pic depends on whether a VOA(M\, v) is constructible. The constructibility
  of VOA(M\, v) is also equivalent to the partition-representability of M o
 ver an alphabet with cardinality v\, defined by Fero Matúš\, which gener
 alize the linear representability of a matroid over a field.\n\nIn this pa
 rt\, we characterize all matroidal entropy functions with ground set size 
 not exceeding 5 except for log v · r_{U_{2\,5}} and log v · r_{U_{3\,5}}
  for some v. We also briefly discuss the application of matroidal entropy 
 functions to network coding and secret sharing.\n
LOCATION:https://researchseminars.org/talk/AAIT/43/
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