Generalized Hockey Stick Theorem
Molly Lynch, Michael Weselcouch
TL;DR
This paper presents a combinatorial proof of a new identity that generalizes the Hockey Stick Identity and the Big Hockey Stick and Pucks Identity, expanding understanding of binomial coefficient identities.
Contribution
It introduces a novel combinatorial proof using a sign-reversing involution for a generalized hockey stick identity.
Findings
Established a new combinatorial identity generalizing known hockey stick identities.
Provided a sign-reversing involution proof technique for the identity.
Enhanced combinatorial methods for binomial coefficient identities.
Abstract
We give a combinatorial proof via a sign-reversing involution for a new identity that generalizes both the Hockey Stick Identity and the Big Hockey Stick and Pucks Identity.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Genome Rearrangement Algorithms · Limits and Structures in Graph Theory