Geodesic
A Note on Combinatorial Identities for Partial Sums
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 65-67

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For a sequence σ = (x 1, ..., xn ) of real numbers, let σi and respectively denote the cyclic permutation (xi , x i+1, ..., x i-1) and the reverse cyclic permutation (xj , x j-1, ..., x j+1), and let . Also denote by M rj (σ) and mrj (σ) the rth largest and the rth smallest numbers respectively, among the first j partial sums s 1, s 2, ..., Sj for 1≤r≤j≤n. As usual, let the superscripts + and — respectively mean maximize and minimize with zero. 
Mohanty, S. G. A Note on Combinatorial Identities for Partial Sums. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 65-67. doi: 10.4153/CMB-1971-012-8
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     title = {A {Note} on {Combinatorial} {Identities} for {Partial} {Sums}},
     journal = {Canadian mathematical bulletin},
     pages = {65--67},
     year = {1971},
     volume = {14},
     number = {1},
     doi = {10.4153/CMB-1971-012-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-012-8/}
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