TL;DR
This paper provides a bijective proof of the reduced lecture hall partition theorem, extends this bijection to the lecture hall partition theorem, and presents refined versions of these theorems.
Contribution
It introduces a new bijective proof and extends it to broader lecture hall partition theorems with refined versions.
Findings
Bijection proof of the reduced lecture hall partition theorem
Extension of the bijection to the lecture hall partition theorem
Refined versions of both theorems are presented
Abstract
In this paper, we give a bijective proof of the reduced lecture hall partition theorem. It is possible to extend this bijection in lecture hall partition theorem. And refined versions of each theorems are also presented.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Advanced Algebra and Geometry