Parity theorems for statistics on permutations and Catalan words.
Parity-alternating permutations and successions
The study of parity-alternating permutations of {1, 2, … n} is extended to permutations containing a prescribed number of parity successions - adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using direct construction and elementary combinatorial techniques. Analogous results are derived for circular permutations....
Parking functions and noncrossing partitions.
Partial complements and transposable dispersions.
Partial sums of two quartic -series.
Partially Ordered Sets and the Rogers-Ramanujan Identities.
Partitions, q-Series and the Lusztig-Macdonald-Wall Conjectures.
Pattern avoidance classes and subpermutations.
Pattern avoidance in coloured permutations.
Pattern avoidance in matrices.
Pattern avoidance in partial permutations.
Pattern avoidance in permutations: Linear and cyclic orders.
Pattern avoiding partitions and Motzkin left factors
Let L n, n ≥ 1, denote the sequence which counts the number of paths from the origin to the line x = n − 1 using (1, 1), (1, −1), and (1, 0) steps that never dip below the x-axis (called Motzkin left factors). The numbers L n count, among other things, certain restricted subsets of permutations and Catalan paths. In this paper, we provide new combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify four classes of the partitions of size n, all...
Pebblings.
Perfect matchings for the three-term Gale-Robinson sequences.
Periodicity and parity theorems for a statistic on -mino arrangements.
Periodicity in quasipolynomial convolution.
Permutation patterns and continued fractions.
Permutations avoiding an increasing number of length-increasing forbidden subsequences.
Permutations avoiding two patterns of length three.