Seidel triangle sequences and Bi-Entringer numbers
نویسندگان
چکیده
En hommagè a Pierre Rosenstiehl, Lui, qui dirige avec grand style, Ce journal de combinatoire, Mais sait aussì a l'occasion Nous raconter une belle histoire: Fil d'Ariane et boustrophédon. Abstract. This Seidel Triangle Sequence Calculus makes it possible to derive several three-variate generating functions, in particular for the Bi-Entringer numbers, which count the alternating permutations according to their lengths, first and last letters. The paper has been motivated by this suprising observation: the number of alternating permutations, whose last letter has a prescribed value and is greater than its first letter, is equal to the Poupard number.
منابع مشابه
A New Operation on Sequences: The Boustrophedon Transform
A generalization of the Seidel-Entringer-Arnold method for calculating the alternating permutation numbers (or secant-tangent numbers) leads to a new operation on sequences, the boustrophedon transform. This paper was published (in a somewhat different form) in J. Combinatorial Theory, Series A, 76 (1996), pp. 44–54. Present address: Mathematics Department, MIT, Cambridge, MA Present address: A...
متن کاملEvaluation of Bi-objective Scheduling Problems by FDH, Distance and Triangle Methods
In this paper, two methods named distance and triangle methods are extended to evaluate the quality of approximation of the Pareto set from solving bi-objective problems. In order to use evaluation methods, a bi-objective problem is needed to define. It is considered the problem of scheduling jobs in a hybrid flow shop environment with sequence-dependent setup times and the objectives of minimi...
متن کاملEvaluation of Bi-objective Scheduling Problems by FDH, Distance and Triangle Methods
In this paper, two methods named distance and triangle methods are extended to evaluate the quality of approximation of the Pareto set from solving bi-objective problems. In order to use evaluation methods, a bi-objective problem is needed to define. It is considered the problem of scheduling jobs in a hybrid flow shop environment with sequence-dependent setup times and the objectives of minimi...
متن کاملThe median Genocchi numbers, q-analogues and continued fractions
0. Introduction The Genocchi numbers appear in many different contexts (see e.g. [1,4,5,7,6,14,20]). Probably the most well-known definition uses the Seidel triangle 155 155 17 17 155 310 3 3 17 34 138 448 1 1 3 6 14 48 104 552 1 1 1 2 2 8 8 56 56 608 By definition, the triangle is formedby the numbers gk,n (k is the number of a row counted frombottom to top and n is the number of a column from...
متن کاملBijections for Entringer families
André proved that the number of alternating permutations on {1, 2, ..., n} is equal to the Euler number En. A refinement of André’s result was given by Entringer, who proved that counting alternating permutations according to the first element gives rise to Seidel’s triangle (En,k) for computing the Euler numbers. In a series of papers, using generating function method and induction, Poupard ga...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 42 شماره
صفحات -
تاریخ انتشار 2014