منابع مشابه
Avoiding (m, m, m)-Arrays of Order n=2k
An (m,m,m)-array of order n is an n×n array such that each cell is assigned a set of at most m symbols from {1, . . . , n} such that no symbol occurs more than m times in any row or column. An (m,m,m)-array is called avoidable if there exists a Latin square such that no cell in the Latin square contains a symbol that also belongs to the set assigned to the corresponding cell in the array. We sh...
متن کاملOn avoiding some families of arrays
An n × n array A with entries from {1, . . . , n} is avoidable if there is an n × n Latin square L such that no cell in L contains a symbol that occurs in the corresponding cell in A. We show that the problem of determining whether an array that contains at most two entries per cell is avoidable is NP-complete, even in the case when the array has entries from only two distinct symbols. Assuming...
متن کاملThe intricacy of avoiding arrays is 2
Let A be any n× n array on the symbols [n], with at most one symbol in each cell. An n× n Latin square L avoids A if all entries in L differ from the corresponding entries in A. If A is split into two arrays B and C in a special way, there are Latin squares LB and LC avoiding B and C, respectively. In other words, the intricacy of avoiding arrays is 2, the number of arrays into which A has to b...
متن کاملMmm Camments
Number 51 Recently, President Reagan signed a bill to reduce federal spending over the next three years by $130 billion. Almost as soon as the ink dried, Administration officials announced that further reductions totaling about $75 billion were needed to erase the federal budget deficit by 1984. Subsequently, it became evident that even that was not enough. It is clear that these budget plans w...
متن کاملThe Weak Order on Pattern-avoiding Permutations
The weak order on the symmetric group is a well-known partial order which is also a lattice. We consider subposets of the weak order consisting of permutations avoiding a single pattern, characterizing the patterns for which the subposet is a lattice. These patterns have only a single small ascent or descent. We prove that all patterns for which the subposet is a sublattice have length at most ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2167