The number-theoretic content of the Jacobi triple product identity.
The Order of Points on the Second Convex Hull of a Simple Polygon.
The -adic valuations of sequences counting alternating sign matrices.
The packing density of other layered permutations.
The Parity of Permutations.
The partially ordered set of all J-classes of a finite semigroup.
The permutation classes equinumerous to the smooth class.
The Pfaffian transform.
The polynomial part of a restricted partition function related to the Frobenius problem.
The power of a prime that divides a generalized binomial coefficient.
The problem of kings.
The problem of the kings.
The Pythagorean Approach to Problems of Periodicity in Chemistry and Nuclear Physics
The -binomial theorem and two symmetric -identities.
The -Bell numbers.
The ratio and generating function of cogrowth coefficients of finitely generated groups
Let G be a group generated by r elements . Among the reduced words in of length n some, say , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of has a limit, called the cogrowth exponent with respect to the generators . We show by analytic methods that the numbers vary regularly, i.e. the ratio is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function associated...
The reciprocal super Catalan matrix
The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.
The Redheffer matrix of a partially ordered set.
The Schubert calculus of decomposable permutations. (Le calcul de Schubert des permutations décomposables.)