Some partition problems related to the Stirling numbers of the second kind
Some postage stamp 2-bases.
Some problems in number theory, combinatorics and combinatorial geometry.
Some problems of combinatorial number theory related to Bertrand's postulate.
Some problems on splittings of groups.
Some properties of a certain nonaveraging sequence.
Some properties of Buck's measure density
Some properties of the multiple binomial transform and the Hankel transform of shifted sequences.
Some properties of the singular words of the Fibonacci word.
Some q-analogs of congruences for central binomial sums
We establish q-analogs for four congruences involving central binomial coefficients. The q-identities necessary for this purpose are shown via the q-WZ method.
Some q-supercongruences for truncated basic hypergeometric series
For any odd prime p we obtain q-analogues of van Hamme’s and Rodriguez-Villegas’ supercongruences involving products of three binomial coefficients such as for p≡ 3 (mod 4), for p≡ 2 (mod 3), where and . We also prove q-analogues of the Sun brothers’ generalizations of the above supercongruences. Our proofs are elementary in nature and use the theory of basic hypergeometric series and combinatorial q-binomial identities including a new q-Clausen type summation formula.
Some recurrence relations for Cauchy numbers of the first kind.
Some relationships between the analogs of Euler numbers and polynomials.
Some remarks on an identity of Catalan concerning the Fibonacci numbers
Some remarks on differentiable sequences and recursivity.
Some remarks on the equation in Fibonacci numbers.
Some remarks on the Erdős-Turán conjecture
Some remarks on the Lüroth expansion
Some results for generalized harmonic numbers.
Some results for sums of the inverses of binomial coefficients.