Specialty
The study uses spectral and character-based calculations to separate graph constructions where proper fractional revival is impossible from those where exact algebraic conditions allow it.
Scientific publication4 min read
A mathematical preprint reports that the difference in facet counts between chain and order polytopes is exactly the sum of local star-element weights. It also classifies gaps of zero, one and two, and derives a corresponding formula for admissible decompositions in a regular marked setting.
Scientific publication4 min read
A mathematics preprint develops exact identities connecting partial permutations, class functions and forgotten symmetric functions. Its formulas lead to ribbon-tiling and rim-hook descriptions of irreducible-character evaluations, while a cancellation argument narrows one set-mapping calculation to partitions with at most two parts.
Scientific publication5 min read
A mathematical preprint reports a theorem showing that a positive gap below the three-quarter minimum-degree threshold is enough to rule out nonsynchronized local minima in the Kuramoto energy landscape. The result applies to finite simple graphs and does not specify the size of the gap.
Scientific publication4 min read
A mathematical preprint establishes the existence of a degree threshold guaranteeing vertex-disjoint directed cycles with pairwise different lengths. It also gives weighted extensions while leaving the sharpest possible threshold open.
Scientific publication5 min read
An arXiv preprint reports a universal bound between two graph-theory quantities, presents a constructive approximation algorithm, and gives examples showing why the factor two may be impossible to improve.
Scientific publication4 min read
A theoretical graph-theory preprint identifies an exact finiteness dichotomy for one family of forbidden-induced-subgraph classes, then supplies related finite, infinite and algorithmic results.
Scientific publication4 min read
A theory paper presents a canonical block-triangular decomposition for finite, connected, simple bipartite graphs. Its results connect the characteristic m to matching extension, structural classes and a lattice of independent sets, while leaving practical runtime performance untested.
Scientific publication5 min read
A deterministic graph-theory result identifies the exact minimum semidegree for prescribed directed 3q-cycles in the stated range, while leaving the best size cutoff unresolved.
Scientific publication3 min read
An arXiv preprint classifies four exceptional Deza graph constructions arising from tangent, secant and external-line relations on quadrics. It gives their exact parameters and structural descriptions, but leaves the full classification of relation unions in higher odd dimensions open.
Scientific publication4 min read
A new arXiv preprint constructs an infinite family of simple, exactly regular expanding graphs whose longest cycles cover less than a chosen fraction of all vertices. The result shows that regularity and sublinear expansion alone do not force a cycle covering every vertex, while leaving open whether stronger degree conditions at the logarithmic-square scale guarantee Hamiltonicity.
Scientific publication5 min read
A theorem-based study of formal infinite words finds a complete ternary spectrum, dense level sets for alphabets of at least three symbols, and sharply different behavior in rotation and polynomial codings.
Scientific publication3 min read
An arXiv proof note derives two deterministic upper bounds for nonempty, regular, increasing, 3-wise intersecting families of subsets. The sharper form uses the Lambert W function; a simpler Fourier argument gives a weaker bound.
Scientific publication4 min read
A proof-based arXiv preprint studies permutations with exactly k cycles. In the stated range, it identifies the largest intersecting families as stars and gives asymptotic bounds for families that are not centred.
Scientific publication4 min read
A mathematical preprint reports a stronger rigorous lower bound for the growth rate of the permutation class Av(1324). Its final construction produces a selected value above 10.629, while interval-certified calculations support the theorem's conservative bound of 10.617.
Scientific publication4 min read
A theorem-driven preprint broadens Kahn–Lovász-type counting results to F-factors and related edge-constrained problems. It presents an asymptotically sharp result for Hamiltonian patterns, alongside bounds for a selected connected class and loopless multigraphs.
Scientific publication3 min read