Half-simple symmetric Venn diagrams.
Handshakes across a (round) table.
Hankel determinants and the Sylvester theorem. (Déterminants de Hankel et théorème de Sylvester.)
Higher chain formula proved by combinatorics.
Hybrid proofs of the -binomial theorem and other identities.
HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Improved bounds for and the factorical polynomial.
Improved bounds on the number of ways of expressing as a binomial coefficient.
Integer sequences and matrices over finite fields.
Integral representations and binomial coefficients.
Integral representations of Catalan and related numbers.
Integrals and polygamma representations for binomial sums.
Integrals of logarithmic and hypergeometric functions
Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. In this paper we explore many relations and explicitly derive closed form representations of integrals of logarithmic, hypergeometric functions and the Lerch phi transcendent in terms of zeta functions and sums of alternating harmonic numbers.
Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.
Inversions of permutations in symmetric, alternating, and dihedral groups.
Jensen proof of a curious binomial identity.
k-Tuples of the First n Natural Numbers.
Legendre polynomials and supercongruences
Let p > 3 be a prime, and let Rₚ be the set of rational numbers whose denominator is not divisible by p. Let Pₙ(x) be the Legendre polynomials. In this paper we mainly show that for m,n,t ∈ Rₚ with m≢ 0 (mod p), and , where (a/p) is the Legendre symbol and [x] is the greatest integer function. As an application we solve some conjectures of Z. W. Sun and the author concerning , where m is an integer not divisible by p.
Mahler's expansion and Boolean functions.
Mappings of Acyclic and Parking Functions.