The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A248475

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Number of pairs of partitions of n that are successors in reverse lexicographic order, but incomparable in dominance (natural, majorization) ordering.
(history; published version)

#23 by Peter Luschny at Tue Apr 10 14:29:38 EDT 2018

STATUS

reviewed

#22 by Andrey Zabolotskiy at Sat Apr 07 17:46:41 EDT 2018

STATUS

proposed

#21 by John M. Campbell at Fri Mar 30 23:37:03 EDT 2018

STATUS

editing

Discussion

Sat Apr 07

17:46

Andrey Zabolotskiy: OK, thank you.

#20 by John M. Campbell at Fri Mar 30 23:36:41 EDT 2018

COMMENTS

Empirical: a(n) is the number of zeros in the subdiagonal of the matrix of coefficients giving the expansion of degree-n complete homogeneous symmetric functions in the Schur basis of the algebra of symmetric functions. - John M. Campbell, Mar 18 2018

#19 by John M. Campbell at Fri Mar 30 23:35:50 EDT 2018

CROSSREFS

Cf. A182988, A248476.

#18 by John M. Campbell at Fri Mar 30 23:34:40 EDT 2018

COMMENTS

Equivalently, a(n) is the number of zeros in the subdiagonal of the matrix of coefficients giving the expansion of degree-n complete homogeneous symmetric functions in the Schur basis of the algebra of symmetric functions. - John M. Campbell, Mar 18 2018

STATUS

proposed

#17 by Andrey Zabolotskiy at Thu Mar 29 13:45:21 EDT 2018

STATUS

editing

Discussion

Fri Mar 30

23:34

John M. Campbell: @Zabolotskiy Thank you for your feedback. I should've noted that my proposed comments are "Empirical". I'll add cross-references in A248475 to the other two sequences. I think that the ordering of the basis elements according to the inverse lexicographic ordering is fairly standard.

#16 by Andrey Zabolotskiy at Thu Mar 29 13:45:15 EDT 2018

MATHEMATICA

Needs["Combinatorica`];

STATUS

proposed

#15 by Jon E. Schoenfield at Sun Mar 18 22:03:52 EDT 2018

STATUS

editing

Discussion

Thu Mar 29

13:44

Andrey Zabolotskiy: Nice. Three questions: 1. Are all three proposed comments proven? 2. Perhaps add cross-references to other two sequences? 3. Is the ordering of the basis elements corresponding to the inverse lexicographic ordering of the corresponding partitions somewhat canonical? If no, perhaps it would be better to say "the lower-triangular matrix" to eliminate the ambiguity.

#14 by Jon E. Schoenfield at Sun Mar 18 22:03:48 EDT 2018

COMMENTS

Equivalently, a(n) is the number of zeroes in the sub-diagonal of the matrix of coefficients giving the expansion of degree-n complete homogeneous symmetric functions in the Schur basis of the algebra of symmetric functions. - John M. Campbell, Mar 18 2018

STATUS

proposed