Two New Integer Sequences Related to Crossroads and Catalan Numbers
Julien Rouyer and Alain Ninet
Laboratoire de Mathématiques de Reims (LMR) - CNRS UMR 9008
Université de Reims Champagne-Ardenne
U.F.R. Sciences Exactes et Naturelles
Moulin de la Housse - BP 1039
51687 Reims cedex 2
France
Abstract:
The marriageable singles sequence represents the number of noncrossing
partitions of the finite set {1, ..., n} in which some pair of
singleton blocks can be joined while remaining noncrossing. The lonely
singles sequence represents the number of all the other noncrossing
partitions of the finite set {1, ..., n} and is the difference between
the Catalan numbers sequence and the marriageable singles sequence. The
first 16 terms of these sequences are given, as well as some of their
properties. These sequences appear when one wants to count the number
of ways to cross certain road intersections simultaneously.
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(Concerned with sequences
A000108
A363448
A363449.)
Received November 11 2023; revised versions received November 12 2023; November 13 2023; February 12 2024; October 1 2024.
Published in Journal of Integer Sequences,
January 3 2025.
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