The On-Line Encyclopedia of Integer Sequences (OEIS)

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A115722

Table of Durfee square of partitions in Mathematica order.
(history; published version)

#10 by Susanna Cuyler at Fri Jan 17 10:36:20 EST 2020

STATUS

proposed

approved

#9 by Michel Marcus at Fri Jan 17 10:05:43 EST 2020

STATUS

editing

proposed

#8 by Michel Marcus at Fri Jan 17 10:05:28 EST 2020

EXAMPLE

First few rows: 0; 1,1; 1,1,1; 1,1,2,1,1; 1,1,2,1,2,1,1

First few rows:

0;

1,1;

1,1,1;

1,1,2,1,1;

1,1,2,1,2,1,1;

STATUS

proposed

editing

#7 by Michael De Vlieger at Fri Jan 17 09:27:29 EST 2020

STATUS

editing

proposed

#6 by Michael De Vlieger at Fri Jan 17 09:27:18 EST 2020

LINKS

Michael De Vlieger, <a href="/A115722/b115722.txt">Table of n, a(n) for n = 0..11731</a> (rows 0 <= n <= 26).

MATHEMATICA

{0}~Join~Array[Map[Block[{k = Length@ #}, While[Nand[k > 0, AllTrue[Take[#, k], # >= k &]], k--]; k] &, IntegerPartitions@ #] &, 10] // Flatten (* Michael De Vlieger, Jan 17 2020 *)

#5 by Michael De Vlieger at Fri Jan 17 09:23:53 EST 2020

LINKS

Michael De Vlieger, <a href="/A115722/b115722.txt">Table of n, a(n) for n = 0..11731</a>

STATUS

approved

editing

#4 by Russ Cox at Sat Mar 31 13:21:30 EDT 2012

AUTHOR

Frank _Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), _, Mar 11 2006

Discussion

Sat Mar 31

13:21

OEIS Server: https://oeis.org/edit/global/884

#3 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

LINKS

E. W. Eric Weisstein, 's World of Mathematics, <a href="http://mathworld.wolfram.com/DurfeeSquare.html">Durfee Square.</a>

KEYWORD

nonn,tabf,new

#2 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

KEYWORD

nonn,tabl,newtabf

#1 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

NAME

Table of Durfee square of partitions in Mathematica order.

DATA

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2

OFFSET

0,10

LINKS

E. W. Weisstein, <a href="http://mathworld.wolfram.com/DurfeeSquare.html">Durfee Square.</a>

FORMULA

If partition is laid out in descending order p(1),p(2),...,p(k) without repetition factors (e.g. [3,2,2,1,1,1]), a(P) = max_k min(k,p(k)).

EXAMPLE

First few rows: 0; 1,1; 1,1,1; 1,1,2,1,1; 1,1,2,1,2,1,1

CROSSREFS

Cf. A115721, A115994, A115720, A080577.

Row lengths A000041, totals A115995.

KEYWORD

nonn,tabl

AUTHOR

Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 11 2006

STATUS

approved