AbstractWe characterize sequences of positive integers (m1,…,mp),m1⩾…⩾mp>0, for which the productn×k(ofn-element andk-element chains),n⩾k, can be partitioned into chainsC1,…,Cpsuch that |Ci|=mi, fori=1,…,p. The main result says that such a partition exists if and only if ∑ji=1mi⩽∑ji=1(k+n+1−2i), forj=1,…,kand ∑pi=1mimi=nk
AbstractThe principal result of this paper establishes the validity of a conjecture by Graham and Ro...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, …, n} o...
AbstractIn this paper the following theorem is proved and generalized. The partitions of any positiv...
AbstractWe characterize sequences of positive integers (m1,…,mp),m1⩾…⩾mp>0, for which the productn×k...
Given a sequence A = (a1, …, an) of real numbers, a block B of A is either a set B = {ai, ai+1, …, a...
AbstractWe consider the sums of m increasing products from a sequence 〈Xt〉t = 1∞, denoted SPm(〈xt〉t ...
AbstractWe present a bijection between non-crossing partitions of the set [2n+1] into n+1 blocks suc...
AbstractA sequence m1≥m2≥⋯≥mk of k positive integers isn-realizable if there is a partition X1,X2,…,...
AbstractFor any partially ordered set P, let dk(P)(d̂k(P)) denote the cardinality of the largest sub...
A method is given for finding a chain of maximum length between two partitions λ ⩽ μ in the lattice ...
AbstractWe characterize all numbers n and S with the following property: Every instance of the parti...
AbstractWe introduce the notion of arithmetic progression blocks or m-AP-blocks of Zn, which can be ...
AbstractA procedure for partitioning the collection of divisors of an integer into symmetric chains ...
AbstractGeneralizing a classical problem in enumerative combinatorics, Mansour and Sun counted the n...
AbstractA general theorem for providing a class of combinatorial identities where the sum is over al...
AbstractThe principal result of this paper establishes the validity of a conjecture by Graham and Ro...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, …, n} o...
AbstractIn this paper the following theorem is proved and generalized. The partitions of any positiv...
AbstractWe characterize sequences of positive integers (m1,…,mp),m1⩾…⩾mp>0, for which the productn×k...
Given a sequence A = (a1, …, an) of real numbers, a block B of A is either a set B = {ai, ai+1, …, a...
AbstractWe consider the sums of m increasing products from a sequence 〈Xt〉t = 1∞, denoted SPm(〈xt〉t ...
AbstractWe present a bijection between non-crossing partitions of the set [2n+1] into n+1 blocks suc...
AbstractA sequence m1≥m2≥⋯≥mk of k positive integers isn-realizable if there is a partition X1,X2,…,...
AbstractFor any partially ordered set P, let dk(P)(d̂k(P)) denote the cardinality of the largest sub...
A method is given for finding a chain of maximum length between two partitions λ ⩽ μ in the lattice ...
AbstractWe characterize all numbers n and S with the following property: Every instance of the parti...
AbstractWe introduce the notion of arithmetic progression blocks or m-AP-blocks of Zn, which can be ...
AbstractA procedure for partitioning the collection of divisors of an integer into symmetric chains ...
AbstractGeneralizing a classical problem in enumerative combinatorics, Mansour and Sun counted the n...
AbstractA general theorem for providing a class of combinatorial identities where the sum is over al...
AbstractThe principal result of this paper establishes the validity of a conjecture by Graham and Ro...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, …, n} o...
AbstractIn this paper the following theorem is proved and generalized. The partitions of any positiv...
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