29 citations · 154 across the 72 of their papers we have counts for
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A unifying generalization of Sperner's theorem
Matthias Beck, Xueqin Wang, Thomas Zaslavsky
Sperner's bound on the size of an antichain in the lattice P(S) of subsets of a finite set S has been generalized in three different directions: by Erdos to subsets of P(S) in whic…
Dedekind sums: a combinatorial-geometric viewpoint
Matthias Beck, Sinai Robins
The literature on Dedekind sums is vast. In this expository paper we show that there is a common thread to many generalizations of Dedekind sums, namely through the study of lattic…
A Meshalkin theorem for projective geometries
Matthias Beck, Thomas Zaslavsky
Let M be a family of sequences (a_1,...,a_p) where each a_k is a flat in a projective geometry of rank n (dimension n-1) and order q, and the sum of ranks, r(a_1) + ... + r(a_p), e…
A shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains
Matthias Beck, Thomas Zaslavsky
Meshalkin's theorem states that a class of ordered p-partitions of an n-set has at most members if for each k the k'th parts form an antichain. We giv…
Multidimensional Ehrhart Reciprocity
Matthias Beck
In a previous paper (El. J. Combin. 6 (1999), R37), the author generalized Ehrhart's idea of counting lattice points in dilated rational polytopes: Given a rational polytope, that…
Explicit and efficient formulas for the lattice point count in rational polygons using Dedekind-Rademacher sums
Matthias Beck, Sinai Robins
We give explicit, polynomial-time computable formulas for the number of integer points in any two-dimensional rational polygon. A rational polygon is one whose vertices have ration…
Arithmetic partition sums and orbits of Z_n^k under the symmetric group S_k
Matthias Beck, Alex J. Feingold, Michael D. Weiner
We study M(n,k,r), the number of orbits of {(a_1,...,a_k)\in Z_n^k | a_1+...+a_k = r (mod n)} under the action of S_k. Equivalently, M(n,k,r) sums the partition numbers of an arith…