Add constant 41b - Ambidextrous Moving Sofa Constant

README.md

@@ -73,7 +73,8 @@ Bounds for which the level of available verification is currently at minimal lev
 | [39](https://teorth.github.io/optimizationproblems/constants/39a.html) | Hadwiger covering / illumination number in $\mathbb{R}^3$ | 8 | 14 |
 | [40a](https://teorth.github.io/optimizationproblems/constants/40a.html) | Lehmer’s Mahler measure constant | 1 | 1.176280... |
 | [40b](https://teorth.github.io/optimizationproblems/constants/40b.html) | Asymptotic Dobrowolski constant for Lehmer’s problem | $9/4$ | $\infty$ |
-| [41](https://teorth.github.io/optimizationproblems/constants/41a.html) | Moving sofa constant | 2.2195 | 2.37 (2.2195*)|
+| [41a](https://teorth.github.io/optimizationproblems/constants/41a.html) | Moving sofa constant | 2.2195 | 2.37 (2.2195*)|
+| [41b](https://teorth.github.io/optimizationproblems/constants/41a.html) | Ambidextrous moving sofa constant | 1.64495521 | 2.2195 |
 | [42](https://teorth.github.io/optimizationproblems/constants/42a.html) | Turan's pure power sum constant | 0.5 | 0.69368 |
 | [43](https://teorth.github.io/optimizationproblems/constants/43a.html) | Gilbert-Pollak conjecture (Steiner ratio) | 0.8559 | 0.86602540378 |
 | [44](https://teorth.github.io/optimizationproblems/constants/44a.html) | Maximal number of relevant variables in degree-$d$ Boolean functions | 1.5 | 4.394 |

constants/41a.md

@@ -2,7 +2,7 @@
 
 ## Description of constant
 
-The moving sofa constant $C\_{41}=A$ is the maximum area of a connected, rigid planar shape that can maneuver through an L-shaped corridor of unit width.
+The moving sofa constant $C\_{41a}=A$ is the maximum area of a connected, rigid planar shape that can maneuver through an L-shaped corridor of unit width.
 The corridor is formed by two semi-infinite strips of width 1 meeting at a right angle.
 The problem asks for the shape of the largest area (the "sofa") that can be moved from one end of the corridor to the other by a continuous rigid motion (translation and rotation).
 

constants/41b.md

@@ -0,0 +1,44 @@
+# Ambidextrous Moving Sofa Constant
+
+## Description of constant
+
+The ambidextrous moving sofa constant $C\_{41b}$ asks for the maximum area of a sofa, as defined in $C\_{41a}$ that can navigate both left and right corners inside a Z-shaped corridor of width 1, where the corners are sufficiently far apart.
+That is, the shape of the largest area (the "sofa") that can be moved from one end of the corridor to the other by a continuous rigid motion (translation and rotation).
+Trivially, $C\_{41a} \ge \_{41b}$
+
+## Known upper bounds
+
+| Bound | Reference | Comments |
+| ----- | --------- | -------- |
+| $2 \sqrt{2}$ | [Hammersley1968] | Intended for $C\_{41a}$, but can be modified for $C\_{41b}$ |
+| 2.2195 | [Baek2024] | Naive bound from $C\_{41a}$ |
+
+## Known lower bounds
+
+| Bound | Reference | Comments |
+| ----- | --------- | -------- |
+| 1.64495 | [Gibbs2014] | Numerical result |
+| 1.64495521 | [Romik2016] |  |
+
+## Additional comments
+- [Wikipedia section](https://en.wikipedia.org/wiki/Moving_sofa_problem#Ambidextrous_sofa)
+- Another question posed by Conway considers a T-shaped intersection. It is unknown whether the two problems are equivalent.
+
+
+## References
+
+- [Baek2024] Baek, J. (2024).
+Optimality of Gerver's Sofa.
+[arXiv:2411.19826](https://arxiv.org/abs/2411.19826).
+
+- [Gibbs2014] Philip Gibbs (2014).
+A Computational Study of Sofas and Cars.
+[vixra:1411.0038v2](https://vixra.org/pdf/1411.0038v2.pdf).
+
+- [Hammersley1968] J. M. Hammersley (1968).
+On the enfeeblement of mathematical skills by modern mathematics and by similar soft intellectual trash in schools and universities. Bulletin of the Institute of Mathematics and Its Applications.
+4: 66–85. See Appendix IV, Problems, Problem 8, p. 84.
+
+- [Romik2016] Dan Romik (2016).
+Differential equations and exact solutions in the moving sofa problem.
+[arxiv:1606.08111](https://arxiv.org/abs/1606.08111).