Bijections for hook pair identities.
Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations.
Bijective proofs of identities from colored binary trees.
Binary -words without the subword 1010. . . 10.
Binomial sums via Bailey's cubic transformation
By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the -series, we examine a class of -series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.
Catalan traffic at the beach.
Chapter 8 of Ramanujan's second notebook.
Chromatic statistics for triangulations and Fuß-Catalan complexes.
Circulants and the factorization of the Fibonacci–like numbers
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
Classification of bijections between 321- and 132-avoiding permutations.
Coding parking functions by pairs of permutations.
Combinatorial and automated proofs of certain identities.
Combinatorial aspects of code loops
The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T. Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E. Goodaire contained in [2]. Within this paper, we focus on their combinatorial construction and prove...
Combinatorial aspects of multiple zeta values.
Combinatorial bases of modules for affine Lie algebra B 2(1)
We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases...
Combinatorial identities by way of Wilf's multigraph model.
Combinatorial identities deriving from the th power of a matrix.
Combinatorial identities from the spectral theory of quantum graphs.
Combinatorial proofs of Capelli's and Turnbull's identities from classical invariant theory.
Combinatorial proofs of some Simons-type binomial coefficient identities.