scholarly journals A new combinatorial identity for unicellular maps, via a direct bijective approach

2011 ◽  
Vol 47 (4) ◽  
pp. 874-893 ◽  
Author(s):  
Guillaume Chapuy
Keyword(s):  
Combinatorial Identity

scholarly journals n-Color partitions with weighted differences equal to minus two

1997 ◽  
Vol 20 (4) ◽  
pp. 759-768 ◽  
Author(s):  
A. K. Agarwal ◽  
R. Balasubrananian
Keyword(s):  
Explicit Expression ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Combinatorial Identities ◽  
Combinatorial Identity ◽  
Divisor Function ◽  
Open Problems

In this paper we study thosen-color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to−2Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables. By using these partitions an explicit expression for the sum of the divisors of odd integers is given. It is shown how these partitions arise in the study of conjugate and self-conjugaten-color partitions. A combinatorial identity for self-conjugaten-color partitions is also obtained. We conclude by posing several open problems in the last section.

scholarly journals A combinatorial identity with application to Catalan numbers

2006 ◽  
Vol 306 (16) ◽  
pp. 1921-1940 ◽  
Author(s):  
Hao Pan ◽  
Zhi-Wei Sun
Keyword(s):  
Catalan Numbers ◽  
Combinatorial Identity

A Remarkable Combinatorial Identity

2012 ◽  
Vol 85 (3) ◽  
pp. 201-205 ◽  
Author(s):  
Mihail Frumosu ◽  
Alexander Teodorescu-Frumosu
Keyword(s):  
Combinatorial Identity

scholarly journals Decomposable graphs and hypergraphs

1984 ◽  
Vol 36 (1) ◽  
pp. 12-29 ◽  
Author(s):  
S. L. Lauritzen ◽  
T. P. Speed ◽  
K. Vijayan
Keyword(s):  
Combinatorial Identity ◽  
Decomposable Graphs

AbstractWe define and investigate the notion of a decomposable hypergraph, showing that such a hypergraph always is conformal, that is, can be viewed as the class of maximal cliques of a graph. We further show that the clique hypergraph of a graph is decomposable if and only if the graph is triangulated and characterise such graphs in terms of a combinatorial identity.

A New Proof of a Combinatorial Identity

1970 ◽  
Vol 43 (3) ◽  
pp. 162-163
Author(s):  
David C. Shipman
Keyword(s):  
Combinatorial Identity

82.14 Equivalence Classes and a Familiar Combinatorial Identity

1998 ◽  
Vol 82 (493) ◽  
pp. 98 ◽  
Author(s):  
Richard Grassl ◽  
Tabitha Mingus
Keyword(s):  
Equivalence Classes ◽  
Combinatorial Identity

scholarly journals A combinatorial identity for the derivative of a theta series of a finite type root lattice

2003 ◽  
Vol 172 ◽  
pp. 1-30
Author(s):  
Satoshi Naito
Keyword(s):  
Representation Theory ◽  
Lie Algebra ◽  
Finite Type ◽  
Cartan Subalgebra ◽  
Theta Series ◽  
Combinatorial Identity ◽  
Root Lattice ◽  
Simple Lie Algebra ◽  
Finite Dimensional ◽  
Affine Lie Algebra

AbstractLet be a (not necessarily simply laced) finite-dimensional complex simple Lie algebra with the Cartan subalgebra and Q ⊂ * the root lattice. Denote by ΘQ(q) the theta series of the root lattice Q of . We prove a curious “combinatorial” identity for the derivative of ΘQ(q), i.e. for by using the representation theory of an affine Lie algebra.

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