Description
Return the forward ratio of adjacent binomial coefficients.
Exact combinatorial recurrences distinguish individual summands, adjacent ratios and complete totals. A local arithmetic identity can be correct without proving that its supplied inputs are the intended counts or that a whole enumeration has been completed.
Return the forward ratio of adjacent binomial coefficients.
When to use this tool
Use Binomial Lattice Step Forward Ratio when checking the stated recurrence, coefficient-ratio or inclusion-exclusion term.
How to use the tool and how it works
- Enter n, k. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio. Use the output convention below.
Return the forward ratio of adjacent binomial coefficients. Require whole n >= 1 and k in [0,n); ratio = (n-k)/(k+1), meaning binomial(n,k+1)/binomial(n,k).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| n | N | Required. Safe integer; minimum 1. |
| k | K | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Ratio | Required. Finite number. |
{
"input": {
"n": 5,
"k": 2
},
"output": {
"ratio": 1
}
}Limitations and assumptions
- The result uses floating point rather than exact coefficient strings; no coefficient or distribution is generated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete recurrence with justified initial conditions and exact integer arithmetic when a full counting result is required.
References
Similar or alternative tools
- Binomial Coefficient Log Ratio Step
Return adjacent binomial ratio and its natural logarithm.
- Combinatorics: Binomial Adjacent Coefficient Ratio
Return one adjacent binomial coefficient ratio.