Complexity of sequences defined by billiard in the cube
Composition of transpositions and equality of ribbon Schur -functions.
Composition sum identities related to the distribution of coordinate values in a discrete simplex.
Compositional inversion of triangular sets of series.
Compositions of graphs revisited.
Compositions of n as alternating sequences of weakly increasing and strictly decreasing partitions
Compositions and partitions of positive integers are often studied in separate frameworks where partitions are given by q-series generating functions and compositions exhibiting specific patterns are designated by generating functions for these patterns. Here, we view compositions as alternating sequences of weakly increasing and strictly decreasing partitions (i.e. alternating blocks). We obtain generating functions for the number of such partitions in terms of the size of the composition, the...
Compositions of random functions on a finite set.
Compositions with distinct parts.
Compression theorems for periodic tilings and consequences.
Computation of -partial fractions.
Computational proofs of congruences for 2-colored Frobenius partitions.
Computing the generating function of a series given its first few terms.
Computing the molecular expansion of species with the Maple package Devmol.
Computing the period of an Ehrhart quasi-polynomial.
Computing tournament sequence numbers efficiently with matrix techniques.
Concave compositions.
Conditions on periodicity for sum-free sets.
Congruence properties for a class of arithmetical functions.
Congruences for a class of alternating lacunary sums of binomial coefficients.
Congruences for certain binomial sums
We exploit the properties of Legendre polynomials defined by the contour integral where the contour encloses the origin and is traversed in the counterclockwise direction, to obtain congruences of certain sums of central binomial coefficients. More explicitly, by comparing various expressions of the values of Legendre polynomials, it can be proved that for any positive integer , a prime and , we have , depending on the value of .