۱۴۰۳ پنج شنبه ۱ آذر

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Preliminary definitions (PDF)
Problem (1): Prove the nonexistence of perfect codes in S_n, using the Kendall τ-metric, for more values of n and/or other distances
 
Articles related to the  Problem (1)
 
Problem (2): What is the size of an optimal anticode in S_n with diameter D
 
Problem (3): Improve the lower bounds on the sizes of codes in S_n with even minimum Kendall τ-distance
  
Problem (4): Can the codes in S_5 and S_7 from Section V be generalized for higher values of n and to larger distances? Are these codes of optimal size
 Note that the auther of the latter paper formulated the calculation of P(n, d) as a binary integer program  with linear/quadratic constraints and found its value
for n ∈ {5, 6}. By using a solver (Gurobi Optimization Inc), the values of P(5, d) for d ∈ {3, 4, 5, 6} and P(6, d) for d ∈ {4, 5, . . . , 10} has been found successfully . But the solver has not been able to find the optimal value of P(6, 3) even after several weeks of computation. The solver has  found a heuristic solution of cardinality 102 improving the lower bound on P(6, 3) from the previous value of 90.  Click here to see 720 constraints of the optimization problem corresponding to  P(6,3).
 
 
تاریخ به روز رسانی:
1401/10/23
تعداد بازدید:
696
دانشگاه اصفهان
آدرس: اصفهان، میدان آزادی، دانشگاه اصفهان  , دانشکده ریاضی و آمار
کدپستی: 73441-81746
E-mail:  a.abdollahi@math.ui.ac.ir
تلفن: 37934600 تلفکس: 36684458
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