Balls on the lawn.
Baxter permutations and plane bipolar orientations.
Bender's generalized q-binominal Vandermonde convolution.
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.