Bijection between bigrassmannian permutations maximal below a permutation and its essential set.
Bijections and congruences for generalizations of partition identities of Euler and Guy.
Bijections for hook pair identities.
Bijective counting of tree-rooted maps and shuffles of parenthesis systems.
Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations.
Bijective proofs of identities from colored binary trees.
Bijective proofs of parity theorems for partition statistics.
Bijective recurrences concerning Schröder paths.
Billiard complexity in the hypercube
We consider the billiard map in the hypercube of . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that is the order of magnitude of the complexity.
Binary -words without the subword 1010. . . 10.
Binary relations on the power set of an -element set.
Binary segmentation and Bonferroni-type bounds
We introduce the function , where and are the pdf and cdf of , respectively. We derive two recurrence formulas for the effective computation of its values. We show that with an algorithm for this function, we can efficiently compute the second-order terms of Bonferroni-type inequalities yielding the upper and lower bounds for the distribution of a max-type binary segmentation statistic in the case of small samples (where asymptotic results do not work), and in general for max-type random variables...
Binary strings without zigzags.
Binary words containing infinitely many overlaps.
Binomial coefficients.
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.
Bipartition orders and statistics on words. (Ordres bipartitionnaires et statistiques sur les mots.)
Blocks for symmetric groups and their covering groups and quadratic forms.
Bonferroni-Galambos inequalities for partition lattices.
Boole's formula as a consequence of Lagrange's interpolating polynomial theorem.