Events
DMS Combinatorics Seminar |
| Time: Sep 10, 2020 (02:00 PM) |
| Location: ZOOM |
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Details: Speaker: Dean Hoffman Title: A combinatorial lemma
Definitions for my 9/10/20 seminar talk The rows of our arrays will be indexed by the set R, with |R| = m; and the columns by the set C, with |C| = n. Each cell will be occupied by a symbol from the set S.
Definition 1 Arrays A and B are said to be row-similar, if for each r R, the multisets of symbols occurring in rows r of A and B are identical.
Definition 2 Array B is said to be column Latin if for all c C, no symbol occurs more than once in column c of B.
Definition 3 The integer vector a = (ac | c C) is balanced, if for all c, d C, |ac – ad | ≤ 1.
Definition 4 If s S, the column census of s in B is the vector VB(s) = (tc | c C), where tc is the number of occurrences of symbol s in column c of B.
Definition 5 We define B to be balanced if VB(s) is balanced for all s S.
Definition 6 A digraph is said to be balanced if for every vertex v, |indegree(v) – outdegree(v)| ≤ 1.
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