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A341850 Array read by antidiagonals: T(n,m) is the number of maximum matchings in the rook graph K_n X K_m. 5
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 3, 4, 4, 3, 1, 1, 15, 16, 72, 16, 15, 1, 1, 15, 56, 132, 132, 56, 15, 1, 1, 105, 376, 7020, 2016, 7020, 376, 105, 1, 1, 105, 1912, 17280, 44928, 44928, 17280, 1912, 105, 1, 1, 945, 17984, 1920240, 1551744, 22615200, 1551744, 1920240, 17984, 945, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,12
COMMENTS
In the case that both m and n are odd a single vertex is not covered, otherwise the maximum matchings are perfect matchings.
LINKS
Eric Weisstein's World of Mathematics, Maximum Independent Edge Set
Eric Weisstein's World of Mathematics, Rook Graph
FORMULA
T(n,m) = T(m,n).
EXAMPLE
Array begins:
======================================================
n\m | 0 1 2 3 4 5 6
----+-------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 1 1 1 3 3 15 15 ...
2 | 1 1 2 4 16 56 376 ...
3 | 1 3 4 72 132 7020 17280 ...
4 | 1 3 16 132 2016 44928 1551744 ...
5 | 1 15 56 7020 44928 22615200 243319680 ...
6 | 1 15 376 17280 1551744 243319680 61903180800 ...
...
CROSSREFS
Rows n=1..4 are A133221(n+1), A081919, A341851, A341852.
Main diagonal is A289197.
Cf. A270227 (matchings), A286070, A341847 (maximal matchings).
Sequence in context: A085747 A106693 A107335 * A341847 A200223 A236228
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 21 2021
STATUS
approved

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Last modified May 18 11:53 EDT 2024. Contains 372630 sequences. (Running on oeis4.)