Parameters in Inversion Sequences-Reference-Cited by-同舟云学术

Parameters in Inversion Sequences

Published:2023-06-01 Issue:3 Volume:73 Page:551-564
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Archibald Margaret¹,Blecher Aubrey¹,Knopfmacher Arnold¹

Affiliation:

1. The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand , Private Bag 3, P O WITS 2050 , Johannesburg , SOUTH AFRICA

Abstract

ABSTRACT We study various combinatorial parameters in the set of inversion sequences of length n. First, we provide generating functions for 1-successions and then generalise this to p-successions. Thereafter we find the formulae for the total number of successions by extracting coefficients. We then do the same for runs of length r and the length of the ith run. Next, we derive a generating function for the number of inversions in inversion sequences themselves and show that inversion sequences with no inversions are counted by the Catalan numbers. Finally, viewing inversion sequences as bargraphs, we develop a generating function for their area.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0041/pdf

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