User RobPratt - Mathematics Stack Exchange

4 votes

Number of ways to color in a $2\times5$ grid

answered Apr 11, 2020 at 2:29

4 votes

Partitions using only powers of two on $1000.$

answered Jul 4, 2020 at 20:48

4 votes

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How to construct a 5-regular graph with diameter 2 on 22 vertices?

answered Jul 5, 2020 at 18:08

4 votes

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Maximum odd number of subsets, each intersects exactly half of the others

answered Mar 14, 2020 at 20:26

4 votes

Solving binomial summation $\sum_{k=0}^{\lfloor{n/2}\rfloor} \binom{n-k}{k} 2^{n-k}$

answered Mar 16, 2020 at 20:17

4 votes

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Are constants allowed within an objective function for a linear programming problem?

answered Mar 28, 2020 at 20:45

4 votes

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calculating total number of allowable paths

answered Apr 2, 2020 at 21:52

4 votes

Number of paths between points in a grid with blocked nodes?

answered Apr 4, 2020 at 0:23

4 votes

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Use of Bijection for computation

answered Feb 14, 2020 at 21:55

4 votes

Provide a combinatorial proof for an identity using the Binomial Theorem

answered Feb 21, 2020 at 19:51

4 votes

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No. of grid walks not going through four points

answered Aug 8, 2020 at 16:52

4 votes

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What is the fastest computational algorithm to find a monochromatic $K_{10}$ in a complete graph?

answered Sep 4, 2020 at 1:13

4 votes

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Dice game - deciding whether to re-roll or not

answered Sep 21, 2020 at 20:37

4 votes

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Counting binary strings of length $n$ that contain no two adjacent blocks of 1s of the same length?

answered Oct 9, 2020 at 22:22

4 votes

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Find minimum number of figures needed , so that no additional figure can be added?

answered Oct 16, 2020 at 14:26

4 votes

Combinatorial Proof for Composite/Nested Binomial Coefficient

answered Oct 17, 2020 at 8:37

4 votes

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Let $f(n)=\sum_{k=0}^{\left\lfloor n/2\right\rfloor} {2k \choose k}{n \choose 2k}$ . Show that $\sum_{n\geq 0}^{} f(n)x^n=\frac{1}{\sqrt{1-2x-3x^2}}$

answered Oct 21, 2020 at 14:09

4 votes

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one optimization problem in matrix multiplication and related recurrence

answered Dec 7, 2020 at 17:42

4 votes

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How to find the series $a_{n}$ which has this generating function: $f(x)=\frac{1}{1-x^{2}}$?

answered Jan 8, 2021 at 23:19

4 votes

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Any nice/good way to allow an "or" option in a linear program?

answered Jan 5, 2021 at 17:11

4 votes

Counting minimum elements needed such that their sum covers the whole finite space.

answered Jan 6, 2021 at 19:20

4 votes

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Linear/Integer Programming: Scheduling task with regular intervals

answered Dec 20, 2020 at 18:03

4 votes

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Probability that a 5-card poker hand contains exactly four cards of the same suit?

answered Oct 29, 2020 at 3:36

4 votes

Only one-way implication

answered Nov 9, 2020 at 21:00

4 votes

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Probability that at least one Ace is dealt in poker with $6$ players

answered Nov 15, 2020 at 18:19

4 votes

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How to create a 4-sided die and an 8-sided die such that the sum follows the same distribution as the sum of 2 standard 6-sided dice?

answered Nov 21, 2020 at 22:07

4 votes

Why is connectedness in the majority of graph theoretical results?

answered Nov 24, 2020 at 21:47

4 votes

Combinatorial proof for $n\ge1$ of $3^n = \sum_{k=0}^n \binom{n}{k}(2^{n-k})$

answered Sep 21, 2021 at 21:27

4 votes

Is it possible to place one queen and at least 29 knights in a 8x8 chess board such that no 2 pieces attack each other?

answered Aug 21, 2021 at 1:06

4 votes

Find the integral solution with minimum sum given the product is constant.

answered Apr 29, 2021 at 2:44

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1,968 Answers

Number of ways to color in a $2\times5$ grid

Partitions using only powers of two on $1000.$

How to construct a 5-regular graph with diameter 2 on 22 vertices?

Maximum odd number of subsets, each intersects exactly half of the others

Solving binomial summation $\sum_{k=0}^{\lfloor{n/2}\rfloor} \binom{n-k}{k} 2^{n-k}$

Are constants allowed within an objective function for a linear programming problem?

calculating total number of allowable paths

Number of paths between points in a grid with blocked nodes?

Use of Bijection for computation

Provide a combinatorial proof for an identity using the Binomial Theorem

No. of grid walks not going through four points

What is the fastest computational algorithm to find a monochromatic $K_{10}$ in a complete graph?

Dice game - deciding whether to re-roll or not

Counting binary strings of length $n$ that contain no two adjacent blocks of 1s of the same length?

Find minimum number of figures needed , so that no additional figure can be added?

Combinatorial Proof for Composite/Nested Binomial Coefficient

Let $f(n)=\sum_{k=0}^{\left\lfloor n/2\right\rfloor} {2k \choose k}{n \choose 2k}$ . Show that $\sum_{n\geq 0}^{} f(n)x^n=\frac{1}{\sqrt{1-2x-3x^2}}$

one optimization problem in matrix multiplication and related recurrence

How to find the series $a_{n}$ which has this generating function: $f(x)=\frac{1}{1-x^{2}}$?

Any nice/good way to allow an "or" option in a linear program?

Counting minimum elements needed such that their sum covers the whole finite space.

Linear/Integer Programming: Scheduling task with regular intervals

Probability that a 5-card poker hand contains exactly four cards of the same suit?

Only one-way implication

Probability that at least one Ace is dealt in poker with $6$ players

How to create a 4-sided die and an 8-sided die such that the sum follows the same distribution as the sum of 2 standard 6-sided dice?

Why is connectedness in the majority of graph theoretical results?

Combinatorial proof for $n\ge1$ of $3^n = \sum_{k=0}^n \binom{n}{k}(2^{n-k})$

Is it possible to place one queen and at least 29 knights in a 8x8 chess board such that no 2 pieces attack each other?

Find the integral solution with minimum sum given the product is constant.