The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A141618 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A141618

Triangle read by rows: number of nilpotent partial transformations (of an n-element set) of height r (height(alpha) = |Im(alpha)|), 0 <= r < n.
(history; published version)

#73 by N. J. A. Sloane at Sun Jun 23 21:22:05 EDT 2024

STATUS

proposed

approved

#72 by Alan Kappler at Sat Jun 08 03:07:03 EDT 2024

STATUS

editing

proposed

#71 by Alan Kappler at Sat Jun 08 03:07:00 EDT 2024

COMMENTS

T(n,k) is the number of parking functions of length n containing exactly k+1 distinct values in its image. - _Alan Kappler_, Jun 08 2024

#70 by Michel Marcus at Sat Jun 08 01:29:10 EDT 2024

STATUS

proposed

editing

#69 by Alan Kappler at Fri Jun 07 19:12:51 EDT 2024

STATUS

editing

proposed

Discussion

Sat Jun 08

01:29

Michel Marcus: please sign new comment: simply append - ~~~~

#68 by Alan Kappler at Fri Jun 07 19:10:38 EDT 2024

COMMENTS

T(n,k) is the number of parking functions of length n containing exactly k+1 distinct values in its image.

STATUS

approved

editing

Discussion

Fri Jun 07

19:12

Alan Kappler: Proof of equality to stirling-number form is through a circle argument (similar to Pollak)

#67 by Joerg Arndt at Mon Nov 23 06:04:26 EST 2020

STATUS

reviewed

approved

#66 by Michel Marcus at Mon Nov 23 05:23:08 EST 2020

STATUS

proposed

reviewed

#65 by Matthieu Josuat-Vergès at Mon Nov 23 05:18:59 EST 2020

STATUS

editing

proposed

#64 by Matthieu Josuat-Vergès at Mon Nov 23 05:18:21 EST 2020

LINKS

A. Laradji and A. Umar, <a href="https://mathfiles.kfupm.edu.sa/data/files/techReportsDatamathonly/TechnicalReportsData/305.pdf">On the number of nilpotents in the partial symmetric semigroup</a>, Tech. Report TR305, King Fahd Univ. of Petroleum and Minerals, (2003).

STATUS

approved

editing