We present a general construction of involutions on integer partitions which enable us to prove a number of modulo 2 partition congru-ences.
Jantzen-Seitz partitions are those p-regular partitions of n which label p-modular irreducible representations of the symmetric group S n which remain irreducible when restricted to S n?1 ; they have recently also been found to be important for certain exactly solvable models in statistical mechanics. In this article we study their combinatorial properties… (More)
— It is known that the two statistics on integer partitions " hook length " and " part length " are equidistributed over the set of all partitions of n. We extend this result by proving that the bivariate joint generating function by those two statistics is symmetric. Our method is based on a generating function by a triple statistic much easier to… (More)
Frieze patterns (in the sense of Conway and Coxeter) are in close connection to triangulations of polygons. Broline, Crowe and Isaacs have assigned a symmetric matrix to each polygon triangulation and computed the determinant. In this paper we consider d-angulations of polygons and generalize the combinatorial algorithm for computing the entries in the… (More)
We classify partitions which are of maximal p-weight for all odd primes p. As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.