We invoke some ideas from finite geometry to map bijectively 135 heptads of mutually commuting three-qubit observables into 135 symmetric four-qubit ones. After labeling the elements of the former set in terms of a seven-dimensional Clifford algebra, we present the bijective map and most pronounced actions of the associated symplectic group on both sets in explicit forms. This formalism is then...

Motivated by a conjecture of Liang [Y.-C. Liang. Anti-magic labeling of graphs. PhD thesis, National Sun Yat-sen University, 2013.], we introduce a restricted path packing problem in bipartite graphs that we call a V-free 2-matching. We verify the conjecture through a weakening of the hypergraph matching problem. We close the paper by showing that it is NP-complete to decide whether one of the ...

Model-generation based theorem provers such as SATCHMO and MGTP suffer from a combinatorial explosion of the search space caused by clauses irrelevant to the goal (negative clause) to be solved. To avoid this, two typical methods have been proposed. One is relevancy testing implemented in SATCHMORE by Loveland et al., and the other is non-Horn magic sets that are the extension of Horn magic set...

We show how high-resolution magic angle-spinning NMR spectroscopy can be used to characterize 13C-labeled saccharides that have been prepared using solid-phase synthesis techniques while they are still bound to a solid-support resin. With the use of 13C-labeled glucose as the starting material, we have successfully synthesized mono-, di- and trisaccharides with uniform 13C labeling of the sacch...

A magic square of order n is an n by n matrix with distinct nonnegative integer entries such that every row sum, column sum, and (two) diagonal sums equals to the same number m, the magic number. Adding 1 to every entry will give us a traditional magic square of positive integers. A magic square is pure if the entries are the consecutive numbers from 0 to n − 1, and hence it has magic number 3 ...

When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of most external path does not affect curve. We strengthen this statement and also make it more concrete by observing factorization property: if $Z^{}_{n+k}$ denotes refined partition function system $n+k$ non-crossing paths, with endpoints $k$ paths possibly displaced, then at...

let g(v,e) be a graph with p vertices and q edges. a graph g is said to have an odd mean labeling if there exists a function f : v (g) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : e(g) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. a graph that admits an odd mean lab...