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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A321893 Sum of coefficients of forgotten symmetric functions in the Schur function of the integer partition with Heinz number n.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 3, 4, 4, 1, 7, 1, 5, 8
Offset: 1

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Author

Gus Wiseman, Nov 20 2018

Keywords

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Examples

			The sum of coefficients of s(32) = f(221) + 2f(2111) + 5f(11111) is a(15) = 8.

Links

Crossrefs

Row sums of A321892.
Cf. A000085, A008480, A056239, A082733, A124794, A124795, A153452, A296150, A296188, A300121, A321742-A321765.

A321894 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in f(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

Original entry on oeis.org

1, 1, -1, 1, 1, 0, 1, -1, 1, -2, 1, 0, -1, 0, 1, -1, 1, 1, 0, 0, 1, 1, -1, 0, 0, 2, -1, -1, 1, 0, 1, -1, 0, 0, 1, -1, 1, -3, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, -1, 1, -2, 1, 1, -1, -1, 1, 0, -2, 2, -1, 1, -1, 0, 0
Offset: 1

Views

Author

Gus Wiseman, Nov 20 2018

Keywords

Comments

Row n has length A000041(A056239(n)).
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Examples

			Triangle begins:
   1
   1
  -1   1
   1   0
   1  -1   1
  -2   1   0
  -1   0   1  -1   1
   1   0   0
   1   1  -1   0   0
   2  -1  -1   1   0
   1  -1   0   0   1  -1   1
  -3   0   1   0   0
  -1   0   1   0   0  -1   0   0   1  -1   1
  -2   1   1  -1  -1   1   0
  -2   2  -1   1  -1   0   0
For example, row 15 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).

Links

Crossrefs

Row sums are A321764.
Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A317552, A321742-A321765, A321892.

A321929 Tetrangle where T(n,H(u),H(v)) is the coefficient of f(v) in s(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

Original entry on oeis.org

1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 0, 1, 3, 0, 1, 1, 2, 3, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 1, 0, 2, 5, 0, 0, 1, 2, 1, 3, 5, 0, 0, 0, 1, 1, 3, 6, 0, 1, 1, 2, 2, 3, 4, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Gus Wiseman, Nov 23 2018

Keywords

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Examples

			Tetrangle begins (zeros not shown):
  (1): 1
.
  (2):    1
  (11): 1 1
.
  (3):       1
  (21):    1 2
  (111): 1 1 1
.
  (4):            1
  (22):     1   1 2
  (31):         1 3
  (211):    1 1 2 3
  (1111): 1 1 1 1 1
.
  (5):                 1
  (41):              1 4
  (32):          1   2 5
  (221):       1 2 1 3 5
  (311):         1 1 3 6
  (2111):    1 1 2 2 3 4
  (11111): 1 1 1 1 1 1 1
For example, row 14 gives: s(32) = f(221) + 2f(2111) + 5f(11111).

Links

Crossrefs

This is a regrouping of the triangle A321892.
Cf. A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
Showing 1-3 of 3 results.

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