A Bijective Proof of Borchardt's Identity
نویسنده
چکیده
We prove Borchardt’s identity det ( 1 xi − yj ) per ( 1 xi − yj ) = det ( 1 (xi − yj) ) by means of sign-reversing involutions.
منابع مشابه
Transforming Inductive Proofs to Bijective Proofs
is not obvious as a relation among the integers, but has a natural bijective explanation. Namely, let Sk be the set of k-subsets of [n]. (Here, [n] denotes the set of positive integers less than or equal to n.) Then |Sk| = n! k!(n−k)! , so the left side of the identity is ∑n k=0 |Sk|. Since the sets Sk are disjoint, this is equal to | ⋃n k=0 Sk| = |P([n])| = 2 , which completes the proof. Of co...
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عنوان ژورنال:
- Electr. J. Comb.
دوره 11 شماره
صفحات -
تاریخ انتشار 2004