For positive integers m and n let L(m, n) denote the set of all m-tuples (a1, a2..., am) of integers with 0≤a1≤a2⋯≤am≤n. The set L(m, n) is partially ordered such that (a1,...,am)≤(b1,... bm) holds precisely when ai ≤ bi for i = 1, 2,..., m.
The partially ordered set L(3, n) has a partition into saturated symmetric chains when n ;a. 0. 2. PROOF OF THE THEOREM. The theorem will be proved by induction ...
A partition of L(3,n) into saturated symmetric chains. Europ. J. Comb., 1 (1980), pp. 61-63. View PDFView articleView in Scopus Google Scholar. [18]. R. Mahnke.
Dec 6, 2022 · We give a constructive proof that Young's lattice L(5, n) has a partition into saturated symmetric chains. Subjects: Combinatorics (math.CO).
The cases of L(3,n) and L(4,n) are also known to have a symmetric chain decom- position [2, 6, 11, 12]; expressing the poset as a disjoint union of saturated ...
A symmetric chain order is one whose elements can be partitioned into chains which are saturated (skip no ranks) and·symmetric about the middle rank.
Mar 17, 2013 · The problem is made easy with the following Lemma. Call a ranked poset P a symmetric chain order if it can be partitioned into symmetric chains.
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MATH 583. ORDER AND OPTIMIZATION, Fall 2009. Summary of Lectures. This page contains a summary of the lectures in this course for Fall 2009.
A Partition of L(3, n) into Saturated Symmetric Chains. Article. Mar 1980 ... We prove that the partially ordered set L (3, n ) has a partition into saturated ...
Jul 29, 2024 · A partition of L ( 3 , n ) L 3 n L(3,n) italic_L ( 3 , italic_n ) into saturated symmetric chains. European J. Combin., 1(1): 61-63 ...