A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions.
A complete grammar for decomposing a family of graphs into 3-connected components.
A concise proof of the Littlewood-Richardson rule.
A Conjecture Concerning The Existence Of Certain Combinatorial Designs.
A conjecture of Biggs concerning the resistance of a distance-regular graph.
A conjecture of Stanley on alternating permutations.
A conjecture on cycle-pancyclism in tournaments
Let T be a hamiltonian tournament with n vertices and γ a hamiltonian cycle of T. In previous works we introduced and studied the concept of cycle-pancyclism to capture the following question: What is the maximum intersection with γ of a cycle of length k? More precisely, for a cycle Cₖ of length k in T we denote , the number of arcs that γ and Cₖ have in common. Let and f(n,k) = minf(k,T,γ)|T is a hamiltonian tournament with n vertices, and γ a hamiltonian cycle of T. In previous papers we gave...
A conjecture on the prevalence of cubic bridge graphs
Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.
A conjectured formula for fully packed loop configurations in a triangle.
A connection between ordinary partitions and tilings with dominoes and squares.
A construction for sets of integers with distinct subset sums.
A construction method for complete sets of mutually orthogonal frequency squares.
A construction method for generalized Room squares.
A construction method for generalized Room squares. (Short Communication).
A construction of geodetic blocks
A construction of large graphs of diameter two and given degree from Abelian lifts of dipoles
For any we construct graphs of degree , diameter , and order , obtained as lifts of dipoles with voltages in cyclic groups. For Cayley Abelian graphs of diameter two a slightly better result of has been known [3] but it applies only to special values of degrees depending on prime powers.
A construction of resolvable quadruple systems
A Constructive Extension of the Characterization on PotentiallyK s , t -Bigraphic Pairs
Let Ks,t be the complete bipartite graph with partite sets of size s and t. Let L1 = ([a1, b1], . . . , [am, bm]) and L2 = ([c1, d1], . . . , [cn, dn]) be two sequences of intervals consisting of nonnegative integers with a1 ≥ a2 ≥ . . . ≥ am and c1 ≥ c2 ≥ . . . ≥ cn. We say that L = (L1; L2) is potentially Ks,t (resp. As,t)-bigraphic if there is a simple bipartite graph G with partite sets X = {x1, . . . , xm} and Y = {y1, . . . , yn} such that ai ≤ dG(xi) ≤ bi for 1 ≤ i ≤ m, ci ≤ dG(yi) ≤ di for...
A continued fraction expansion for a -tangent function.
A continuum of totally incomparable hereditarily indecomposable Banach spaces
A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.