Articles

Articles David Callan

2023

(with Toufik Mansour) Three classes of inversion sequences counted by large Schroder numbers, Aust J. Combin., submitted.
(with Toufik Mansour) Inversion sequences avoiding a quadruple of length-3 patterns, INTEGERS, to appear.
(with Tewodros Amdeberhan) Gaussian Inequality, Rocky Mountain Journal of Mathematics, to appear.
(with Vit Jelinek and Toufik Mansour) Inversion Sequences Avoiding a Triple of Patterns of 3 Letters, The Electronic Journal of Combinatorics, 30(3), Article P3.19, Published 2023-08-11 (39pp).
The number of {1243,2134}-avoiding permutations, Discrete Mathematics & Theoretical Computer Science, 22 no. 2, Permutation Patterns 2019, published on March 03, 2023.
(with Toufik Mansour) Restricted inversion sequences and Schroder paths, Quaestiones Mathematicae, Published online: 03 Feb 2023.

2022

Permutations avoiding 4321 and 3241 have an algebraic generating function, Discrete Mathematics & Theoretical Computer Science, 22 no. 2, Permutation Patterns 2019, published on December 13, 2022.

2021

(with Toufik Mansour and Jose L. Ramirez) Statistics on Bargraphs of Catalan Words, Journal of Automata, Languages and Combinatorics 26 2021 3-4, 177–196.

2019

(with Toufik Mansour and Mark Shattuck) Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done, Pure Math. Appl. (PU.M.A.), 28 Issue 1, 2019, 14–69.

2018

(with Toufik Mansour) Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, Pure Math. Appl. (PU.M.A.), 27 Issue 1, 2018, 32–61.
(with Toufik Mansour) Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns, Pure Math. Appl. (PU.M.A.), 27 Issue 1, 2018, 62–97.
(with Toufik Mansour) Five Subsets of Permutations Enumerated as Weak Sorting Permutations, Southeast Asian Bull. Math., 42 Issue 3, 2018, 327–340.

2017

(with Toufik Mansour and Mark Shattuck) Twelve subsets of permutations enumerated as maximally clustered permutations, Ann. Math. Inform., 47, 2017, 41–74.
(with Toufik Mansour) On permutations avoiding 1324, 2143, and another 4-letter pattern, Pure Math. Appl. (PU.M.A.), 26 Issue 1, 2017, 1–10.
(with Toufik Mansour) On permutations avoiding 1243, 2134, and another 4-letter pattern, Pure Math. Appl. (PU.M.A.), 26 Issue 1, 2017, 11–21.
(with Toufik Mansour and Mark Shattuck) Wilf classification of triples of 4-letter patterns I, Discrete Math. Theor. Comput. Sci., 19, Issue 1, Paper No. 5, 2017, 35pp.
(with Toufik Mansour and Mark Shattuck) Wilf classification of triples of 4-letter patterns II, Discrete Math. Theor. Comput. Sci., 19, Issue 1, Paper No. 6, 2017, 44pp.
(with Tewodros Amdeberhan, Hideyuki Ohtsuka, and Roberto Tauraso) Revitalized automatic proofs: demonstrations, INTEGERS, 17, Paper No. A16, 2017, 12pp.

2016

(with Shi-Mei Ma and Toufik Mansour) Restricted Stirling permutations, Taiwanese J. Math., 20 Issue 5, 2016, 957–978.

2015

(with Shi-Mei Ma and Toufik Mansour) Some combinatorial arrays related to the Lotka-Volterra system, Electron. J. Combin., 22 Paper 2.22, 2015, 12pp.
(with Toufik Mansour and Mark Shattuck) Some identities for derangement and Ward number sequences and related bijections, Pure Math. Appl. (PU.M.A.), 25 Issue 2, 2015, 132–143.

2014

(with Toufik Mansour and Mark Shattuck) Restricted ascent sequences and Catalan numbers, Appl. Anal. Discrete Math., 8 Issue 2, 2014, 288–303.

2013

(with Tewodros Amdeberhan and Victor Moll) Valuations and combinatorics of truncated exponential sums, INTEGERS, 13 Paper A21, 2013, 16pp.

2012

Flexagons Lead to a Catalan Number Identity, American Mathematical Monthly, 119 No. 5, May 2012, 2927–2937.

2011

Lagrange Inversion Counts 35bar241-Avoiding Permutations, J. Integer Seq., 14 no. 9, Article 11.9.4, 2011, 5pp.
(with Emeric Deutsch) The run transform, Discrete Mathematics, 312 Issue 19, 2012, 2927–2937.

2010

A bijection to count (1-23-4)-avoiding permutations, unpublished (15pp).

2009

A combinatorial survey of identities for the double factorial, (29pp).

2008

Card deals, lattice paths, abelian words and combinatorial identities, (10pp).
Klazar trees and perfect matchings, European J. Combinatorics 31 (2010), 1265–1282.
(with Evangelos Georgiadis and Qing-Hu Hou) Circular digraph walks, k-balanced strings, lattice paths and Chebychev polynomials, The Electronic Journal of Combinatorics, 15(1), Article R108, 2008 (12pp).
Pattern avoidance in "flattened" partitions, Discrete Mathematics, 309, Issue 12, 2009, 4187–4191.

2007

A combinatorial interpretation for the identity $Sum_{k=0}^{n} binom{n}{k} Sum_{j=0}^{k} binom{k}{j}^{3}= Sum_{k=0}^{n} binom{n}{k}^{2}binom{2k}{k}$ , Journal of Integer Sequences, 11, Article 08.3.4, 2008.
Sets, lists and noncrossing partitions, Journal of Integer Sequences, 11, Article 08.1.3, 2008.
Bijections from Dyck paths to 321-avoiding permutations revisited.
A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata, Discrete Mathematics & Theoretical Computer Science, 10, Issue 2, 2008.

2006

A bijection on Dyck paths and its cycle structure, The Electronic Journal of Combinatorics, 14(1), Article R28, 2007 (20pp).
On generating functions involving the square root of a polynomial, Journal of Integer Sequences, 10, Article 07.5.2, 2007.
A combinatorial interpretation of j/n*{kn}\choose{n+j}.

2005

(with Len Smiley) Noncrossing partitions under rotation and reflection.
On conjugates for set partitions and integer compositions.
A combinatorial interpretation of the eigensequence for composition, Journal of Integer Sequences, 9, Article 06.1.4, 2006.
Some identities for the Catalan and Fine numbers, Séminaire Lotharingien de Combinatoire, 53, Article B53e, 2005.
Polygon dissections and marked Dyck paths.

2004

A combinatorial interpretation for a super-Catalan recurrence, Journal of Integer Sequences, 8, Article 05.1.8, 2005.
Two bijections for Dyck path parameters.
Some bijections for restricted Motzkin paths.
A combinatorial proof of Sun's ''curious'' identity, INTEGERS, 4 (2004) A5.

2003

A uniformly distributed parameter on a class of lattice paths, The Electronic Journal of Combinatorics, 11(1), Article R82, 2004 (8pp).
A combinatorial derivation of the number of labeled forests, Journal of Integer Sequences, 6, Article 03.4.7, 2003.
Counting stabilized-interval-free permutations, Journal of Integer Sequences, 7, Article 04.1.8, 2004.
(with Helmut Prodinger) An involutory matrix of eigenvectors, Fibonacci Quarterly 41 (May 2003), 105–107.

2002

2000

Certificates of integrality for linear binomials, Fibonacci Quarterly 38 (Aug 2000), 317-325.
Permutations and coin tossing sequences, Mathematics Magazine 74 (Feb 2001), 55–57.

1999

A combinatorial interpretation of a Catalan numbers identity, Mathematics Magazine, 72 (Oct 1999), 295–298.
Two uniformly distributed parameters defining Catalan numbers, American Mathematical Monthly 106 (Dec 1999), 940–941.

1997

An exploratory approach to Kaplansky's lemma leads to a generalized resultant, American Mathematical Monthly 104 (1997), 709-712.
When does m-n divide f(m)-f(n)? A look at column-finite matrices, Fibonacci Quarterly 35 (1997), 290–298.

1995

On evaluating permanents and a matrix of cotangents, Linear and Multilinear Algebra 38 (1995), 193-205.
Research Problem: Elementary divisors of an inversion counting matrix, Linear and Multilinear Algebra 39 (1995), 401-403.
Pair them up! A visual approach to the Chung-Feller Theorem, College Math. Journal 26 (1995), 196–198.

1991

Another determinant condensation formula, Linear and Multilinear Algebra 29 (1991), 93–98.

1985

Another way to discover that $ \sum_{n=1}^{\infty} \frac{1\cdot 3 \cdot 5 \cdots (2n-1)}{n\,2^{n+1}\,n!} = \textrm{ln}\: 2, $ Mathematics Magazine, 58 (Nov 1985), 283–284.

1978

The isomorphisms of unitary groups over noncommutative domains, Journal of Algebra 52 (1978), 475–503.

1976

The generation of Sp(F_2) by transvections, Journal of Algebra 42 (1976), 378–390.