Enumeration of certain sequences
Enumeration of concave integer partitions.
Enumeration of partitions by long rises, levels, and descents.
Enumeration of sequences constrained by the ratio of consecutive parts.
Enumeration of symmetric arrays with different row sums
Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes.
Enumeration of unigraphical partitions.
Episturmian morphisms and a Galois theorem on continued fractions
We associate with a word on a finite alphabet an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of . Then when we deduce, using the sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.
Episturmian morphisms and a Galois theorem on continued fractions
We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w. Then when |A|=2 we deduce, using the Sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.
Equal values of binary forms at integral points
Equality in Pollard's theorem on set addition of congruence classes
Equality of Dedekind sums modulo 8ℤ
Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].
Equations and inequalities involving .
Équations différentielles algébriques
Équations différentielles -adiques. Croissance des solutions, factorisation, indice
Equations diophantiennes exponentielles
Equations diophantiennes exponentielles.
Équations diophantiennes exponentielles
Équations diophantiennes exponentielles
Équations diophantiennes modulo