A061220 Least entry in character table of the symmetric group S_n.

1, -1, -1, -1, -2, -3, -6, -16, -36, -91, -224, -768, -2420, -7854, -22815, -73008, -292864, -1223040, -5002998, -17592960, -67184000, -279734796, -1183614120, -5844883968, -29448258840, -124619677182, -573333075000, -2764864302200, -13664438287500

Offset: 1

Author

Ola Veshta (olaveshta(AT)my-deja.com), May 30 2001

Keywords

• sign
• nice

Comments

The maximal value in the character table is the maximal degree of an irreducible representation of S_n and this is in sequence A003040.

Examples

			a(3) = -1 because the character table of S_3 is / 1 1 1 / 1 1 -1 / 2 -1 0 /.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..35

Crossrefs

Cf. A003040, A006907.

Programs

GAP

A061220 := n -> Minimum(List(Irr(CharacterTable("Symmetric", n)), Minimum)); # Eric M. Schmidt, Feb 18 2013

Maple

seq(min(map(op,[entries(combinat:-character(n))])),n=1..23); # Robert Israel, Mar 31 2016

Mathematica

a[n_] := With[{S = "S" <> ToString[n]}, FiniteGroupData[S, "CharacterTable"] // Flatten // Min]; Array[a, 10] (* Jean-François Alcover, Mar 31 2016 *)

Extensions

Corrected and extended by Vladeta Jovovic, May 20 2003

More terms from Eric M. Schmidt, Feb 18 2013