The phrase "alternate sum" is correct and usable in written English.
It is typically used in mathematical contexts to refer to a specific type of summation where terms are added and subtracted in an alternating fashion.
Example: "To find the alternate sum of the series, we will add the first term, subtract the second, add the third, and so on."
Alternatives: "alternating sum" or "oscillating sum".
If N Ā1, Ā2, · · ·, Ān) is the number of objects possessing none of the properties A1, A2, · · ·, An, then this number can be computed as an alternating sum of sums involving the numbers of objects that possess the properties This is the principle of inclusion and exclusion expressed by Sylvester.
These results follow simply from Hopf's trace formula which states that the alternating sum of traces in homology is equal to the alternating sum of traces on the chains.
Note that Theorem 5.2 can be also obtained from the algebraic alternating sum formula applied to sequence (5.4).
Recently, Michael Z. Spivey gave a combinatorial proof of the alternating sum Open image in new window by applying an involution to certain colored permutations.
Section 2: We give many properties of the unification of the Bernstein-type polynomials: partition of unity, alternating sum, subdivision property.
Remark 3.3 Goldman [6], [[5], Chapter 5, pp.299-306] derived the formula for the alternating sum of the Bernstein basis functions algebraically.
If the cohomology is finite dimensional, then the alternating sum of traces of (He) i is called the Lefschetz number L (e) of e.
Using functional equations, we give new derivations for the sum and alternating sum of the Bernstein basis functions and a formula for the monomials in terms of the Bernstein basis functions.
In addition, Kim [[7], Theorem 1], Kim and Lee [[8], Lemma 2.1] derived the relations between the Euler polynomials E n ( r ) ( x ) of order r using the alternating sum of powers of consecutive integers T k ( n ).
Explicitly, this gives the complex (C_cdot (E)) with terms begin{aligned} C^n E) = coprod _{x in X([n])}E langle [n],x rangle ) end{aligned} (9.12 and the usual differential given by the alternating sum of the face maps.
