Some combinatorial identities.
Some combinatorial problems, connected with product-isomorphisms of binary relations
Some combinatorial properties of conics in the Hjelmslev plane
Some combinatorial results about the operators with jumping nonlinearities
Some combinatorics involving ξ-large sets
We prove a version of the Ramsey theorem for partitions of (increasing) n-tuples. We derive this result from a version of König's infinity lemma for ξ-large trees. Here ξ < ε₀ and the notion of largeness is in the sense of Hardy hierarchy.
Some Comments on the Eigenspaces of Graphs
Some computational formulas for -Nörlund numbers.
Some congruence properties of binomial coefficients and linear second order recurrences.
Some congruences concerning the Bell numbers.
Some congruences for 3-component multipartitions
Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310).
Some congruences involving binomial coefficients
Binomial coefficients and central trinomial coefficients play important roles in combinatorics. Let p > 3 be a prime. We show that , where the central trinomial coefficient Tₙ is the constant term in the expansion of . We also prove three congruences modulo p³ conjectured by Sun, one of which is . In addition, we get some new combinatorial identities.
Some conjectures on perfect graphs
Some connections between Falconer's distance set conjecture and sets of Furstenburg type.
Some Considerations of Fibonacci Permutations
Some constructions of nested balanced equireplicate block designs
arious methods of constructing nested ternary and quaternary efficiency balanced and variance balanced designs are proposed by applying some repetitions of treatments in all possible pairs of treatments. In these designs sub-blocks and super-blocks may form different p-ary designs, where sub-blocks have higher efficiency as compared to super-blocks, i.e., any two elementary treatment contrasts in the sub-blocks can be measured with higher efficiency than any two elementary contrasts in the super-block...
Some constructions of -minimal graphs
Some crossing numbers of products of cycles
The exact values of crossing numbers of the Cartesian products of four special graphs of order five with cycles are given and, in addition, all known crossing numbers of Cartesian products of cycles with connected graphs on five vertices are summarized.
Some cyclic solutions to the three table Oberwolfach problem.
Some debts I owe.
Some design theoretic results on the Conway group .0.