Generating functions for a lattice path model introduced by Deutsch

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2020-04-08 DOI:10.1515/spma-2020-0133

H. Prodinger

引用次数: 2

Abstract

Abstract The lattice path model suggested by E. Deutsch is derived from ordinary Dyck paths, but with additional down-steps of size −3, −5, −7, . . . . For such paths, we find the generating functions of them, according to length, ending at level i, both, when considering them from left to right and from right to left. The generating functions are intrinsically cubic, and thus (for i = 0) in bijection to various objects, like even trees, ternary trees, etc.

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由Deutsch引入的晶格路径模型的生成函数

摘要E.Deutsch提出的格路径模型是从普通的Dyck路径导出的，但有额外的尺寸为−3、−5、−7的下阶。对于这样的路径，当从左到右和从右到左考虑它们时，我们发现它们的生成函数，根据长度，在级别i结束。生成函数本质上是三次的，因此（对于i=0）在对各种对象的双射中，如偶数树、三元树等。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.