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
conjecture, normalized matching property Let 2 [n] denote the Boolean lattice of order n, that is, t...
AbstractFor positive integers l, n, k we say that M = M(n, k) = {n, n + 1, ..., n + k} has an l-part...
AbstractIn this note we prove that for every sequence (mq)q of positive integers and for every real ...
AbstractWe characterize sequences of positive integers (m1,…,mp),m1⩾…⩾mp>0, for which the productn×k...
AbstractWe consider the sums of m increasing products from a sequence 〈Xt〉t = 1∞, denoted SPm(〈xt〉t ...
P = finite partially ordered set (poset) A chain in P = a linearly ordered subset of P. i.e., a0, a1...
AbstractWe introduce the notion of arithmetic progression blocks or m-AP-blocks of Zn, which can be ...
We introduce the notion of arithmetic progression blocks or m-AP-blocks of Zn, which can be represen...
Given a sequence A = (a1, …, an) of real numbers, a block B of A is either a set B = {ai, ai+1, …, a...
For positive integers m and n let L(m, n) denote the set of all m-tuples (a1, a2..., am) of integers...
A set of necessary conditions for the existence of a partition of {1,... ,2m-1, L} into differences ...
AbstractFor any partially ordered set P, let dk(P)(d̂k(P)) denote the cardinality of the largest sub...
AbstractWe present a bijection between non-crossing partitions of the set [2n+1] into n+1 blocks suc...
AbstractLet N be the set of positive integers and A a subset of N. For n∈N, let p(A,n) denote the nu...
A partition λ of a positive integer n is a sequence λ1 λ2 λm 0 of integers such that ∑λi n. F...
conjecture, normalized matching property Let 2 [n] denote the Boolean lattice of order n, that is, t...
AbstractFor positive integers l, n, k we say that M = M(n, k) = {n, n + 1, ..., n + k} has an l-part...
AbstractIn this note we prove that for every sequence (mq)q of positive integers and for every real ...
AbstractWe characterize sequences of positive integers (m1,…,mp),m1⩾…⩾mp>0, for which the productn×k...
AbstractWe consider the sums of m increasing products from a sequence 〈Xt〉t = 1∞, denoted SPm(〈xt〉t ...
P = finite partially ordered set (poset) A chain in P = a linearly ordered subset of P. i.e., a0, a1...
AbstractWe introduce the notion of arithmetic progression blocks or m-AP-blocks of Zn, which can be ...
We introduce the notion of arithmetic progression blocks or m-AP-blocks of Zn, which can be represen...
Given a sequence A = (a1, …, an) of real numbers, a block B of A is either a set B = {ai, ai+1, …, a...
For positive integers m and n let L(m, n) denote the set of all m-tuples (a1, a2..., am) of integers...
A set of necessary conditions for the existence of a partition of {1,... ,2m-1, L} into differences ...
AbstractFor any partially ordered set P, let dk(P)(d̂k(P)) denote the cardinality of the largest sub...
AbstractWe present a bijection between non-crossing partitions of the set [2n+1] into n+1 blocks suc...
AbstractLet N be the set of positive integers and A a subset of N. For n∈N, let p(A,n) denote the nu...
A partition λ of a positive integer n is a sequence λ1 λ2 λm 0 of integers such that ∑λi n. F...
conjecture, normalized matching property Let 2 [n] denote the Boolean lattice of order n, that is, t...
AbstractFor positive integers l, n, k we say that M = M(n, k) = {n, n + 1, ..., n + k} has an l-part...
AbstractIn this note we prove that for every sequence (mq)q of positive integers and for every real ...
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