Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Some identities for derangement and Ward number sequences and related bijections

Some identities for derangement and Ward number sequences and related bijections Abstract We establish an alternating sum identity for three classes of singleton-free set partitions wherein the number of elements minus the number of blocks is fixed: (i) permutations, that is, partitions into cycles, (ii) unrestricted partitions, and (iii) contents-ordered partitions. Both algebraic and combinatorial proofs are given, the latter making use of a sign-changing involution in each ease. As a consequence, combinatorial proofs are found of specific cases of recent identities of Gould et al. involving both kinds of Stirling numbers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pure Mathematics and Applications de Gruyter

Some identities for derangement and Ward number sequences and related bijections

Download PDF
12 pages

Loading next page...
 
/lp/de-gruyter/some-identities-for-derangement-and-ward-number-sequences-and-related-PmYCjhCkCF
Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
1788-800X
eISSN
1788-800X
DOI
10.1515/puma-2015-0013
Publisher site
See Article on Publisher Site

Abstract

Abstract We establish an alternating sum identity for three classes of singleton-free set partitions wherein the number of elements minus the number of blocks is fixed: (i) permutations, that is, partitions into cycles, (ii) unrestricted partitions, and (iii) contents-ordered partitions. Both algebraic and combinatorial proofs are given, the latter making use of a sign-changing involution in each ease. As a consequence, combinatorial proofs are found of specific cases of recent identities of Gould et al. involving both kinds of Stirling numbers.

Journal

Pure Mathematics and Applications – de Gruyter

Published: Dec 1, 2015

References

  • On - Line Encyclopedia of Integer Sequences at http oeis org
    SLOANE
  • AND On certain sums of Stirling numbers with binomial coefficients Integer Art
    GOULD
  • AND On certain sums of Stirling numbers with binomial coefficients Integer Art
    GOULD
  • Note on the numbers of
    CARLITZ
  • Foundation for
    GRAHAM
  • Proofs that Really Count : The Art of Combinatorial Proof Mathematical Association of America
    Benjamin
  • Foundation for
    GRAHAM
  • The representation of numbers and polynomials as sums of fac torials
    WARD
  • An alternate approach to alternating sums : a method to die for
    Benjamin
  • Asymptotic normality of the numbers
    Clark
  • On - Line Encyclopedia of Integer Sequences at http oeis org
    SLOANE
  • AND Commutation Relations Normal Ordering bers an imprint of
    MANSOL
  • Note on the numbers of
    CARLITZ
  • AND Commutation Relations Normal Ordering bers an imprint of
    MANSOL
  • Asymptotic normality of the numbers
    Clark
  • An alternate approach to alternating sums : a method to die for
    Benjamin
  • Proofs that Really Count : The Art of Combinatorial Proof Mathematical Association of America
    Benjamin
  • The representation of numbers and polynomials as sums of fac torials
    WARD