The phrase "a conjecture on" is correct and usable in written English.
It can be used when discussing a hypothesis or speculation regarding a particular topic or subject matter.
Example: "The scientist presented a conjecture on the potential effects of climate change on marine biodiversity."
Alternatives: "a hypothesis about" or "a speculation regarding".
A conjecture on the eigenvalues of a trigonometric matrix is posed with a partial proof given.
Also we propose a conjecture on an α-analogue of the determinant and permanent.
Also, we state a conjecture on the exact value of the remainder term.
The asymptotic results require a conjecture on the rank of a modified square distance matrix.
However, there is a conjecture on independent spanning trees: any n-connected graph has n independent spanning trees rooted at an arbitrary vertex.
Under a slightly stronger integrability condition (I∞) and a conjecture on the Percus Yevick equation we even can prove strong convergence of the corresponding generators.
The asymptotic limits of the topological indices are determined as a function of N. A conjecture previously published on the asymptotic behavior of the Wiener index is experimentally confirmed.
He also solved a conjecture of David Aldous on Up the River problem (with Li-Cheng Tsai).
Conjecture (based on a conjecture of Woodin): Under suitable large cardinal axioms the generic version of ◊ (absoluteness under Coll ω1, R)) implies that H ω2) is Σ22 absolute under countably closed forcing.
In particular, we describe new progress on a conjecture of Viterbo asserting such bounds for exact deformations of the zero section in unit cotangent disk bundles.
One of the affine designs obtained has the same 2-rank as the design of points and planes in AG(3,4), and provides a counter-example to a conjecture of Hamada [On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error-correcting codes, Hiroshima Math. J. 3 (1973) 153 226].
