Published January 11, 2016 | Version v1
Publication Open

Combinatorial Proofs of Addition Formulas

Creators

  • 1. Academy of Mathematics and Systems Science
  • 2. Chinese Academy of Sciences
  • 3. Zhejiang Sci-Tech University
  • 4. Institute of Mathematics, Academia Sinica

Description

In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the $LDU$ decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition formula for weighted large Schröder paths.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

في هذه الورقة، نقدم دليلاً توافقياً على صيغة الجمع لمسارات موتزكين الجزئية المرجحة. تسمح لنا صيغة الجمع بتحديد تحلل $LDU$ لمصفوفة هانكل للتسلسل متعدد الحدود المحدد بواسطة مسارات موتزكين الجزئية المرجحة. كنتيجة مباشرة، نحصل على محدد مصفوفة هانكل لمتواليات اندماجية معينة. بالإضافة إلى ذلك، نحصل على صيغة إضافة لمسارات شرودر الكبيرة المرجحة.

Translated Description (French)

Dans cet article, nous donnons une preuve combinatoire d'une formule d'addition pour les chemins de Motzkin partiels pondérés. La formule d'addition permet de déterminer la décomposition $LDU$ d' une matrice de Hankel de la séquence polynomiale définie par des chemins de Motzkin partiels pondérés. En conséquence directe, nous obtenons le déterminant de la matrice de Hankel de certaines séquences combinatoires. De plus, nous obtenons une formule d'addition pour les grands chemins de Schröder pondérés.

Translated Description (Spanish)

En este documento damos una prueba combinatoria de una fórmula de suma para trayectorias Motzkin parciales ponderadas. La fórmula de adición nos permite determinar la $LDU$ descomposición de una matriz de Hankel de la secuencia polinómica definida por rutas de Motzkin parciales ponderadas. Como consecuencia directa, obtenemos el determinante de la matriz de Hankel de ciertas secuencias combinatorias. Además, obtenemos una fórmula de suma para caminos de Schröder grandes ponderados.

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Additional details

Additional titles

Translated title (Arabic)
البراهين التوافقية لصيغ الجمع
Translated title (French)
Formules combinatoires de preuves d'addition
Translated title (Spanish)
Comprobaciones combinatorias de fórmulas de adición

Identifiers

Other
https://openalex.org/W2233068432
DOI
10.37236/4793

Is supplement to
https://openalex.org/W4324296894 (Other)
https://openalex.org/W4303647955 (Other)
https://openalex.org/W3013460418 (Other)
https://openalex.org/W2999935146 (Other)
https://openalex.org/W2811365892 (Other)
https://openalex.org/W2547957268 (Other)
https://openalex.org/W2509555593 (Other)
https://openalex.org/W2381090488 (Other)
https://openalex.org/W2166066502 (Other)
https://openalex.org/W1902536278 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
China

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