A115320 - OEIS

A115320

Triangle read by rows. Let L(m,n) = largest integer such that if each symbol in an m X n array appears at most L(m,n) times, then the array must have a transversal. Values are shown in this order: L(m,n), n>=2, m=n, n-1, n-2, ...,2.

%I #6 Jan 14 2020 02:26:05

%S 1,2,5,3,3,7,3,4,7,9,4,5,5,8,11

%N Triangle read by rows. Let L(m,n) = largest integer such that if each symbol in an m X n array appears at most L(m,n) times, then the array must have a transversal. Values are shown in this order: L(m,n), n>=2, m=n, n-1, n-2, ...,2.

%H S. K. Stein and S. Szabo, <a href="https://doi.org/10.1016/j.disc.2005.10.024">The number of distinct symbols in sections of rectangular arrays</a>, Discr. Math., 306 (2006), 254-261.

%e Array begins

%e 1

%e 5 2

%e 7 3 3

%e 9 7 4 3

%e 11 8 5 5 4

%e 13 10 8 ...

%Y See A115321 for transposed array.

%K nonn,tabl,more

%O 2,2

%A _N. J. A. Sloane_, Mar 07 2006