منابع مشابه
Almost All Trees have an Even Number of Independent Sets
This paper is devoted to the proof of the surprising fact that almost all trees have an even number of independent vertex subsets (in the sense that the proportion of those trees with an odd number of independent sets tends to 0 as the number of vertices approaches ∞) and to its generalisation to other moduli: for fixed m, the probability that a randomly chosen tree on n vertices has a number o...
متن کاملAlmost all Pauli Channels have non-zero quantum capacities
Quantum transmission rate may be improved by using input of entangled state instead of product state for Pauli channel. Using GHZ state as input for the depolarizing channel (a special Pauli channel), the channel fidelity of non-zero quantum capacity was improved from > 0.81071 to > 0.80944. We will introduce orthogonal and complete code basis to evaluate the coherent information per channel us...
متن کاملExact quantum algorithms have advantage for almost all Boolean functions
It has been proved that almost all n-bit Boolean functions have exact classical query complexity n. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all n-bit Boolean functions can be computed by an exact quantum algorithm with less than n queries. More exactly, we prove that ANDn is the only n-bit Boolean f...
متن کاملAlmost All Friendly Matrices Have Many Obstructions
A symmetric m×m matrix M with entries taken from {0, 1, ∗} gives rise to a graph partition problem, asking whether a graph can be partitioned into m vertex sets matched to the rows (and corresponding columns) of M such that, if Mij = 1, then any two vertices between the corresponding vertex sets are joined by an edge, and if Mij = 0 then any two vertices between the corresponding vertex sets ar...
متن کاملAlmost All Rooted Maps Have Large Representativity
Let M be a map on a surface S. The edge-width of M is the length of a shortest non-contractible cycle of M . The face-width (or, representativity) of M is the smallest number of intersections a noncontractible curve in S has with M . (The edge-width and face-width of a planar map may be de ned to be in nity.) A map is an LEW-embedding if its maximum face valency is less than its edge-width. For...
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: Archiv der Mathematik
سال: 2020
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-020-01476-x